TIME VALUE OF MONEY (TVM) - WordPress.com · 2018-11-20 · ©Prof. Bijaya G. Shrestha TIME VALUE...

©Prof. Bijaya G. Shrestha

TIME VALUE OF MONEY (TVM)

✓ TVM is a concept to understand the value of cash flow occurred at different point of time.

✓ TVM is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity.

✓ Knowledge of the TVM is essential to an understanding of most topics in financial management. It is one of the pertinent tools to make decision in many cases, those related with finance.

✓ Drawing Time Line is the best way to solve the problems manually.

For lump sum cases

The Basic Models of TVM

For Annuity (Present Value) For Annuity (Future Value)

14,134.79

If you deposit Rs.200 permonth into an account thatpays 6.5% compoundedmonthly, how much willyou have after 5 years?

For PMC_MBS Students


TIME VALUE OF MONEY (TVM)

For lump sum cases For Annuity (Present Value) For Annuity (Future Value)

Divide ‘i’ by ‘m’

Multiply ‘n’ with ‘m’

‘m’ represents number of

periods during the year

You bought a Rs.160,000 motorbike with 40 percent downpayment and financed the rest with a four-year loan at 8 percentstated annual interest rate, compounded monthly. What is yourmonthly payment if you start the payment one month after thepurchase?

Rs.2,343.64

Effective Annual Rate Periodic Rate

If the case is annuity dueMultiply the result of

ordinary annuity by (1+ i)



Amortization of Loan

A firm borrows Rs.100,000, and the loan is to be repaid in three equal payments at the end of each of the next three years. The lender charges 6 percent interest rate on the

loan balance that is outstanding at the beginning

of each year. Prepare loan amortization schedule.

YEAR BEGINNING AMOUNT

PAYMENT INTEREST REPAYMENT OF PRINCIPAL

REMAINING BALANCE

Loan Amortization Schedule

Assuming it as EMI payment, try for first 6 months manually

and solve completely with Computer Excel with the help

of amortization template.Rs.37,411

Find PMT first



Perpetuity

A pension fund plan offers you to

deposit a lump sum money today and in

turn you will have any one of the two

benefits:

(i) Receive a lump-sum of Rs 200,000

at the end of year 5.

(ii) Receive a perpetuity of Rs 15,000

a year starting from the next year.

If your appropriate rate of return is 12

percent, which offer is better for

you?

➢ Perpetuity is an infinite stream of

equal payment.

➢ Remember that previously

discussed annuity cases have finite

number of periods.

➢ Perpetuity is also a type of

annuity but it is equal installment at

each equal interval of time,

indefinitely. Therefore, it should

address by following model:

What is Perpetuity

Rs 125,000Rs 113, 485

Make Decision



Solve the Problems

➢ Suppose you could borrow using

either a credit card that charges 1

percent per month or a bank loan

with a 12 percent quoted nominal

(APR) rate that is compounded

quarterly. Which should you

choose?

➢ Bank A pays 8 percent interest,

compounded quarterly, on its

money market account. The

managers of Bank B want its

money market account to equal

Bank A’s effective annual rate

(EAR), but interest is to be

compounded on a monthly basis.

What nominal, or quoted, or APR

rate must Bank B set?EAR of A: 8.24%APR of B: 7.94%

12.6825% 12.5509%



Solve the Problems

➢Assume that it is now January 1, 2018 and

you will need Rs 100,000 on January 1, 2022.

Your bank compounds interest at an 8 percent

annual rate.

a) How much must you deposit on January 1,

2019, to have a balance of Rs 100,000 on

January 1, 2022?

b) If you want to make equal payments on each

January 1 from 2019 through 2022 to

accumulate the Rs 100,000, how large must

each of the 4 payments be?

c) To help you reach your Rs 100, 000 goal,

your father offers to give you Rs 40,000 on

January 1, 2019. Suppose, you will get a job

and make 6 additional payments of equal

amounts each 6 months thereafter. If all of

this money is deposited in a bank that pays 8

percent, compounded semiannually, how

large must each of the 6 payments be?

79,383

22,192

7,446



APPLICATION OF TIME VALUE OF MONEY

Following are the expected after-tax net cash flows of mutually exclusive

two projects: Investment in Cash Crop Farming or Animal Husbandry.

Make a decision, which project is financially best, suppose that your cost

of capital is 10 percent?

Year (t) Crop farming

Animal husbandry

0 -100,000 -100,000

1 50,000 10,000

2 40,000 30,000

3 30,000 40,000

4 10,000 60,000



APPLICATION OF TIME VALUE OF MONEY

❑Bond is a long-term debt instrument. It is a long-term promissory note issued by a business or governmental unit. The issuer receives money in exchange for promising to make interest

payments and to repay the principal on a specified future date.

❑For the discussion of valuation model, we consider the following types of bond. However, there are many other types.

➢ Perpetual Bond: A bond without specified maturity period and pay interest indefinitely. But no obligation to repay the principal. So this bond is also called irredeemable bond.

➢ Zero Coupon Bond: A bond without coupon interest and sold at substantial discount. The bondholders do not get any interest during the holding period but get fair return through capital gain.

➢ Coupon bonds with a finite maturity: An investor gets periodic interest during maturity period and redeem the face value at the end of maturity.

Perpetual Bonds

BOND VALUATION

Zero Coupon BondsCoupon Bonds with a Finite Maturity



KEY CHARACTERISTICS OF BOND

Par Value: The face value of a bond

Coupon Interest Rate: The stated interest rate on a bond for the coupon payment.

Maturity Date: A specified date on which the par value of a bond must repaid.

Call Provision: Right of issuer to redeem the bonds prior to the normal maturity date.

Sinking Funds: It facilitates the orderly retirement of the bonds each year.

Other Features: Convertible bond, Warrant (Long term option to buy shares as

specified), Putable bond (allow the bond’s investor to sell back to the company prior to

the maturity), Income bond, Indexed (Purchasing Power) bond.

The specific character of the bond depends on the bond contract (indenture).

Unlike the coupon interest rate, which is fixed, the bond’s yield varies from day to day

depending on current market condition. It results Premium or Discount bond.

➢Yield to Maturity (YTM): The rate of return earned on a bond if it is held to maturity.

➢Yield to Call (YTC): The rate of return earned on a bond if it is called before its maturity.

➢Current Yield: The annual interest payment divided by the bond’s current price.

➢Capital Gains Yield: YTM (Total Yield) minus Current Yield.

BOND YIELDS



NUMERICAL APPROACH OF BOND VALUATION

Perpetual Bonds

BOND VALUATION MODELS

Zero Coupon BondsCoupon Bonds with a Finite Maturity

or

Interpolation is required after

approximate YTM

Yield to Call (YTC) means the rate of return

earned on a bond if it is called before its maturity

date.



NUMERICAL APPROACH OF BOND VALUATION

A reputed company issued a new series of bonds on January 1, 1989. The bonds

were sold at par i.e., Rs 1,000, have a 12 percent coupon, and mature in 30 years, on

December 31, 2018. Coupon payments are made semiannually (on June 30 and

December 31).

a) What was the YTM of bonds on January 1, 1989?

b) What was the price of the bond on January 1, 1994, 5 years later, assuming that

the level of interest rates had fallen to 10 percent?

c) Find the current yield and capital gains yield on the bond on January 1, 1994,

given the price as determined in part b.

d) On July1, 2012, bonds sold for Rs 916.42. What was the YTM at that date?

e) What were the current yield and capital gains yield on July1, 2012?

SAMPLE PROBLEMS

12%

Rs 1,182.56

CY =10.15%; CGY = -0.15%

14%

13.09%; 0.91%



RISKINESS OF A BOND

Interest Rate Risk: The risk of a decline in a bond’s price due to an increase in interest

rates (market rate).

The longer the maturity of the bond, the more its price changes in response to a given

change in interest rates.

Reinvestment Rate Risk: The risk of a decline in income from a bond portfolio (new) due

to decline in interest rates.

An increase in interest rates (market rate) will hurt bondholders because it will lead to

a decline in the value of a bond portfolio. But can a decrease in interest rates also

hurt bondholders?

The answer is YES.

Because it will lead to a decline in income from the new investment made. If someone

holding shorter maturity and callable bonds, they suffer furthermore.

Interest rate risk relates to the value of the bonds in a portfolio, while reinvestment risk

relates to the income the portfolio produces.

➢If we hold long-term bonds, we will face interest rate risk. Value of bond decreases.

➢On the other hand, if we hold short-term bonds, we will not be exposed to much interest

rate risk. But we will face Reinvestment Rate Risk.


BOND VALUATION: A Problem for Discussion

Mr. Ashish Sharma is vice president of Nepal Metal Works Inc. The company isconsidering issuing bonds to satisfy part of its financing need for a new venture of SteelPlant, which is going to be launched in Mid-Western Region of Nepal. He knows thatNepalese Financial Market is sensitive to the price and terms and condition of bondissue. As a result of this fact he is reluctant to entertain with new issue. As a financialconsultant, he is seeking your help on certain issues associated with bond contractfeatures, price and yields. You are required to address the following issues on behalf ofMr. Sharma.

a. What are the key features of a bond?b. What are call provisions and sinking fund provisions? Do these provisions makebonds more or less risky?c. How is the value of a bond determined? What is the value of a 10-year,Rs 1,000 par value bond with a 10 percent annual coupon if its required rate of returnis 10 percent?d. What would be the value of the bond described in part 'c' if, just after it had beenissued, the expected inflation rate rose by 3 percentage points, causing investors torequire a 13 percent return? Would we now have a discount or a premium bond?e. What would happen to the bond’s value if inflation fell and kd declined to 7 percent?Would we now have a premium or a discount bond?




f. What would happen to the value of the 10-year bond over time if the required rate of return remained (i) at 13 percent, (ii) at 7 percent? g. What is the yield to maturity on a 10-year, 9 percent, annual coupon, Rs 1,000 par value bond that sells for Rs 887? That sells for Rs 1,134.20? What does the fact that bond sells at a discount or at a premium tells you about the relationship between kd and bond’s coupon rate?h. What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.)i. How would the composition of capital gain yield and current yield for a discount bond changes over the time?




Case Solution Guidelines:

a. Bonds have a number of features. Some of the features are general and some others are specific in nature. General features of bonds consist of par value, coupon rate and the maturity. Specific features of bond include call provision, conversion feature, and sinking fund provision. Specific features largely depend on bond contract (indenture).

b. A call provision gives the issuer the right to call the bonds prior to maturity. Generally, a company pays the bondholders an amount greater than the par value if they are called before maturity. The amount that is paid to the bondholder is called call price and the excess amount over par value is called call premium. When interest rate in the market decreases, bonds having call provision are called up to redeem back with call price to the bondholders before bonds mature. Hence call provision increases risk to the bondholders.

Sinking fund provision is a special provision in a bond contract that facilitates the orderly retirement of the bond. In some cases, the firm may be required to deposit money with trustee, which invests the funds and then uses the accumulated sum to redeem the bonds at maturity. Failing to meet the sinking fund requirement is equivalent to default. Thus, sinking fund provision makes the bond issue less risky.




c. Value of a bond determined as the present value of future stream of interest payment plus present value of maturity value all discounted at bondholders’ required rate of return. The value of a 10-year, Rs 1,000 par value bond with a 10 percent annual coupon, if its required rate of return is 10 percent, is equal to Rs 1,000 par value because bond’s coupon rate is equal to the required rate of return. In other words, if coupon rate is equal to the required return on bond, the bond sells at a premium. d. If required rate of return increases to 13 percent just after the bond issue, the value of bond will decline, which is as follows:Vd= I × PVIFAkd, n + M × PVIFkd, n

= Rs 100 × PVIFA13%, 10 + Rs 1‚000 × PVIF13%,10

= Rs 100 × 5.4262 + Rs 1‚000 × 0.2946 = Rs 542.62 + Rs 294.6 = Rs 837.22 Now we would have a discount bond because the bond will sell below par value. e. If required rate of return declines to 7 percent just after the bond issue, the value of bond will increase, which is as follows:Vd= I × PVIFAkd, n + M × PVIFkd, n

= Rs 100 × PVIFA7%, 10 + Rs 1‚000 × PVIF7%,10

= Rs 100 × 7.0236 + Rs 1‚000 × 0.5083 = Rs 702.36 + Rs 508.3 = Rs 1,210.66 Now we would have a premium bond because the bond will sell above par value.




f. (i) If interest rate remains at 13 percent until maturity, the value of discount bond goes on increasing over time as it approaches to the maturity. Finally, it increases to Rs 1,000 maturity value at the maturity.(ii) If interest rate remains at 7 percent until maturity, the value of premium bond goes on decreasing over time as it approaches to the maturity. Finally, it declines to Rs 1,000 maturity value at the maturity.g. Yield to maturity on a 10-year, 9 percent, annual coupon, Rs 1,000 par value bond that sells for Rs 887.

Given:Annual coupon (I) = 0.09 x Rs 1,000 = Rs 90Maturity value (M) = Rs 1,000Bond’s price (Vd) = Rs 887Time to maturity (n) = 10-year.The yield to maturity on the bond is:

The bond yields about 10.96 percent.

Note that 10.96% is only an approximate YTM. Try to find

out exact YTM by interpolation.




Yield to maturity on a 10-year, 9 percent, annual coupon, Rs 1,000 par value bond that sells for Rs 1,134.20

Given:Annual coupon (I) = 0.09 x Rs 1,000 = Rs 90Maturity value (M) = Rs 1,000Bond’s price (Vd) = Rs 1,134.20Time to maturity (n) = 10-year.

= 0.0703 or 7.03%The bond yields about 7.03 percent.

The relationship between required rate and coupon rate determines whether a bond sells at premium or discount. If required rate is higher than coupon rate, the bond sells at discount. Conversely, if required rate is lower than coupon rate, the bond sells at premium.

Note that 7.03% is only an approximate YTM. Try to find

out exact YTM by interpolation.




h. The total return on the discount bond is the yield to maturity, which is 10.96%. The current yield is calculated as:Current yield = Annual coupon payment/Price of the bond=Rs 90/Rs 887= 0.1015 or 10.15%

The capital gain yield = YTM – Current yield = 10.96% - 10.15% = 0.81%

i. The value of discount bond goes on increasing over the years as it approaches to the maturity. Therefore, for a discount bond, current yield goes on declining and capital gain goes on increasing, but total yield remains at 10.96 percent over the years.




PREFERRED STOCK

➢ Preferred stock is a hybrid security having some characteristics of debt and some of equity.

It also represents the long-term source of financing.

➢The name implies that it has priority over common stock in claims on income and asset.

➢ Like common stock, preferred stock is legally considered as ownership capital.

➢ Generally, it issue without specified maturity date. However, it can be issued with maturity

as well.

➢ Dividend is paid out of after-tax profit.

➢ Preferred dividend is distributed after payment of interest but before common dividend.

➢ Nonpayment of dividends does not force the company into bankruptcy.

➢ Preferred stock can be a cumulative or non-cumulative in nature regarding dividend.

➢ Like bonds, preferred stock dividends are fixed in amount and it always have par value.

➢ In general preferred stockholders do not have the right to vote for the company’s BOD.

➢ Preferred stocks are often callable. Therefore, sinking fund provision can also be arranged.

➢ Conversion feature can also be arranged by the company with preferred stock.

➢Adjustable-rate and Payment-in-kind (PIK) preferred stock are also in practice.

NUMERICAL APPROACH of valuing preferred stock is quite similar to the bond

valuation models.


TIME VALUE OF MONEY (TVM) - WordPress.com · 2018-11-20 · ©Prof. Bijaya G. Shrestha TIME VALUE...

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Transcript of TIME VALUE OF MONEY (TVM) - WordPress.com · 2018-11-20 · ©Prof. Bijaya G. Shrestha TIME VALUE...