Valuation Modeling

7/30/2019 Valuation Modeling

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Valuation basics-Time Value of Money

1 Future Value of one-time cash flow Excel FunctionPrincipal(pv) 100000

Interest ( r ) 0.09

Term(n) 5

Future Value(FV) fv=pv(1+r)n=FV(r,n,0,-pv)

2 Multi-period CompoundingPrincipal(pv) 100000

Interest ( r ) 0.09

Term(n) 5

Number of compounding(m) 2

Future Value(FV) pv*(1+(r/m))(nm)

=FV(r/m,n*m,0,-pv)

3

Continuous Compounding('m' tends to infinity)Principal(PV) 100000

Interest ( r ) 0.09

Term(n) 5

Number of compounding(m) continuous

Future Value(FV) PV * er n

=pv*exp(r n)e=2.7183

3(a) Write a user-defined function for computing the future value at continuously compunded rate, given the pres

4 Effective yield

Interest( r)Number of compounding(m)

Effective yield(ey) (1+(r/m))m-1 =effect(r,m)

4(a) Write a user defined function for calculating the effective yield using excel's inbuilt function "Effect"

4(b) Effective YieldInterest 12.00%continuous compounding rate =exp( r )-1

5 Effecitive Continuous yield

Rs.1000 becomes Rs.1200 in one year with two compounding periods

Compute the normal return and continuous return

Normal return r=(fv/pv)(1/n)-1 =RATE(n,0,-pv,fv)

continuous return =LN(FV/pv)

6 Future value of annuityPrincipal(pv)

Interest( r )



Term (n)Future value(fv) fv=pv((1+r)n-1/r) =FV(r,n,-pmt)

7 Future value of annuity(payments made at the beginning)

Principal(pv)

Interest( r )Term (n)Future value(fv) =FV(r,n,-pmt,0,1)

8 Future value of annuity-applications You need Rs. 30,00,000 in 15 years time to replace an asset. You have to save ever

amount for this and invest at a rate of 15%. How much should you save every year Annuity 63051.15794 4487.613562

Interest 0.15 0.0125

Term 15 180.00Future value $3,000,000.00 $3,000,000.00

8(a) Write a macro to determine the amount to be invested every year for accumulating Rs.3000000 in 15 years9 Present value of a one-time cash flow

Future(fv)Interest ( r )Term(n)Present Value(PV) pv=fv/(1+r)^n =PV(r,n,0,-fv)

10 Present value of AnnuityPrincipal(p)

Interest( r )

Term(n)Present value annuity p(1-1/(1+r)n)/r =pv(r,n,-p)

11 Growing Annuity You rent a office space where the rent currently is 20000 a year. The rate of inflation is 3 %. What isvalue of rentals to be paid over the next five years if the discount rate is 10%?

Principal(p) 20000

Interest ( r ) 0.1

Term(n) 5

Growth rate in annuity(g) 0.03

Present value pv=p(1+g)[(1-(1+g)

n

/(1+r)

n

)/(r-g)] User defined function

12 Continuous Discounting e-rt=FV*EXP(-rt)

13 Generate the following future value tables for Rs.1

n 5.00% 6.00%



1 1.05 1.06

2 1.10 1.123 1.16 1.194 1.22 1.26

14 Perpetuity(contant cash flows for ever) pv=c/r

15 Perpetuity(growing) pv=c(1+g)/(r-g)

EXERCISES IN THE TIME VALUE OF M

(1) Calculate the present value of an annuity of Rs.2000, at 10%, for 20 years.

17,027.13

(2) You are thinking of buying a Rs.1000, five-year bond paying Rs.50 semi-annuallis sold to yield 4% semi-annually. Determine the price you are willing to pay for th

$1,081.11

(3) A sum of Rs.2345 is invested every year for 14 years, at 12% rate of interest. W

is the future value of this investment?

(4) What is the future value of Rs.10,000, invested at 15% for 12 years, with quarterl

compounding?

(5) A sum of Rs.12,000 invested today, becomes Rs.220,000 after 13 years. What is

interest rate on this investment?

25%

(6) In how many months can you accumulate Rs. 5000, by making a monthly paym

Rs.50, at 6% per annum?

50



0.005

81.30

(7) In how many years will Rs.2000 grow to Rs.10,000, at 10% rate of interest?

2000

0.1

(8) You need 2 million in eight years time. If you can invest your money at 7%, how

should you invest today to earn 2 million in 8 years?

(9) How much is 50000 worth at 6 percent compounded continuously after 10 years

$91,105.94

(10) You are comparing interest rates on several loans. First loan has a stated interestrate of 8% with compounding occuring every month. The second loan has a stated interest rate of 7

weekly compounding. The third loan has a stated interest rate of 7.5% with continuous compoundinthe cheapest?

Annual frequencyLoan 1 8.00% 12Loan 2 7.80% 52Loan 3 7.50% 365

(11) An individual sets aside 2000 Dollars athe end of every year, starting when he is 25 years old, fo

retirement age of 65 and he expects to make 8% a year on his investments. If the income tax rate iswhat will be expected value of the account on his retirement? What will be the value of the account iinvestments were made at the beginning of the year?

(12) How much would you need to save each year for the next 40 years to arrive at a future value of saved at the beginning of each year instead of at end?(at 8% interest)

(13) You have the choice of buying a copier for 11000 cash down or paying 3000 a year for five year rate is 12%, which option is cheaper?



(14) A lottery pays out 40 million for the winner over 20 years at the rate of 2 million per year. It hadof 35 million. How is the lottery feasible of the ticket sale value is lower than the lottery value?

(15) Pension obligation of a company is as follows: Years Annual Cash flow

1-5 2006-10 300

11-20 400

At a 10 percent discount rate, what is the present value of the obligations?

$758.16$706.14 $1,137.24

Rs. 947.60Rs. 2,411.89

(16) You are trying to buy a new car that has a price of 15000. The dealer offers you two options.

Option-1: Borrow 15000 at a special rate of 3% p.a for 36 monthsOption-2: You can borrow 14000 at the normal financing rate of 12% p.a for 36 months with a downpayment of 1000Which is a cheaper deal?

(17) You have the rights to a gold mine for the next 20 years, during which you plan to extract 5000of gold every year. The current price per ounce is 300 but it is expected o increase 3% a year. Assuthe discount rate is 10%, what is the present value of the gold mine?

5000 300

(18) If Disneyland generated 100 million in cash flows for Disney last year, the discount rate is 12 %the expected inflation rate is 3%, what is the present value of the cash flows?

What are your assumptions?



(19) You are 55 years old and plan to retire at 60. You intend to start a retirement account. Starting f you intend making some investments which will earn 8% interest. You want to withdraw 30000 annueight years after retirement. How much should you deposit annually into this account?

(20) Rs.1000 becomes Rs.1500 in one year and nine months. What is the continuous compound inte

(21) what is the rate of interest on a a loan of Rs.84000, to be paid in 36 instalments of Rs.3240 per i



63051.15794

0.15

15

153,862.40

$3,000,000.00

155,296.94

156831.22

ent value

0.122 6 12 365

12.36% 12.62% 12.68% 12.75%

12.36%

12.75%

19.09%

18.23%

10000

0.09



559,847.11

10,000.00

0.09

5.00

65,233.35

year some

at 15 % using goal seek function

1000000.07

762,274.97

10000 9500

0.09 0.09

6 7

44,859.19 47,813.05

he present

82454

1000005

0.09 Rs. 64,993.14 63762.81516

7.00% 8.00% 9.00%



1.07 1.08 1.09

1.14 1.17 1.191.23 1.26 1.301.31 1.36 1.41

100000.1 100000

10000

0.030.1 147142.8571

ONEY

, whichbond.

at

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nt of



Rs. 5,000.00

much

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.8% with

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Effective rate8.30%8.11%7.79%

r an expected

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. If the discount



ticket sale

Rs. 2,457.83

uncese that

15000000.03

0.120

16145979.98

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Valuation Modeling

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