Individual Assignment Subject: Corporate Finance

1. Vernox wishes to borrow $10’000 for three years. A group of individuals

agrees to lend him this amount if he contracts to pay them $16’000 at the end of the

three years. What is the implicit compound annual interest rate implied by this

contract (to the nearest whole percent)? (10 marks)

Time line:

0 1 2 3

PV=10.000_ _ _ _ _ _ _ _ _ _FV= 16.000

The Future value of initial $10000 for three years:

FV3= PV (1+i)3

The implicit compound annual interest rate implied by this contract:

(1+i)3= FV3/ PV =16.000/10.000=1.6

1+i=1.61/3

i= 1.61/3-1= 1,169-1=0,169=16,9%

2. Joe has inherited $25’000 and wishes to purchase an annuity that will provide him

with a steady income over the next 12 years. He has heard that the local savings and loan

association is currently paying 6 percent compound interest on annual basis. If he were to

deposit his funds, what year-end equal-dollar amount (to the nearest dollar) would he be

able to withdraw annually such that he would have a zero balance after his last

withdrawal 12 years from now? (10 marks)

0 1 2 3 4 5 6 7 8 9 10 11 12 Year

i=6%

PVA n =25.000 FV=0

The present value of ordinary annuity that Joe has inherited:1

Individual Assignment Subject: Corporate Finance

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1 - (1+i)n

PVA n= PMT x

i

(1 + i)n –1

PVA n= PMT x =

i(1 + i)n

The year-end equal-dollar amount that he be able to withdraw annually:

PMT= PVA n x i(1 + i)n = 25.000x 6% (1+6%)12

(1 + i)n –1 (1+6%)12-1

= $2982

3. Gonzalez Company has outstanding a 10% bond issue with a face value of

$1000 per bond and three years to maturity. Interest is payable annually. The bonds

are privately held by Suresafe Insurance Company. Suresafe wishes to sell the

bonds, and is negotiating with another party. It estimates that, in current market

conditions, the bond should provide a (nominal annual) return of 14 percent. (20

marks).

a. What price per bond should Suresafe be able to realize on the sale?

M=100

INT = 10% x 1000 = 100

n=3

0 1 2 3

100 100 100

1000

PV1

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Individual Assignment Subject: Corporate Finance

PV2

PV3

The price per bond should Suresafe be able to realize on the sale:

VB = INT(1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 100 x (1+14%) 3 -1 + 1000

14% (1+14%) 3 (1+14%) 3

= $ 907, 1

b. What would be the price per bond if interest payment were made semiannually?

M=1000

INT = (10% x 1000)/2 = 50

n=3x2=6

i nom= 0.14

i per=14%/2=7%

0 1 2 3 4 5 6

50 50 50 50 50 50

1000

PV1

PV2

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Individual Assignment Subject: Corporate Finance

PV3

PV4

PV5

PV6

VB = INT(1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 50 x (1+7%) 6 -1 + 1000

14% (1+14%) 6 (1+7%) 6

= $ 904,6

4. Red Brewery has $1’000-par value bonds outstanding with the following

characteristics: currently selling at par; 5 years until final maturity; and a 9 percent

coupon rate (with interest paid semiannually). Interestingly, Blue Brewery has a

very similar bond issue outstanding. In fact, every bond feature is the same as Red

bonds, except that Blue’ bonds mature in exactly 15 years. Now assume that the

market’s nominal annual required rate of return for both bond issues suddenly fell

from 9 percent to 8 percent. (20 marks)

a. Which brewery’s bonds would show the greatest price change? Why?

When coupon rate = 9% . Coupon rate= r d , both bonds sell at its par value ($1000)

INT Red= INT Blue = M x i % = 1000* (9% / 2) = 1000 x 0.45 = 45

n= 5*2= 10

VB Red = INT (1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 45 x (1+0.45) 10 -1 + 1000

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Individual Assignment Subject: Corporate Finance

4.5% (1+4.5%) 10 (1+4.5%) 10

= $ 1000

VB Blue = INT(1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 45 x (1+4.5 %) 30 -1 + 1000

0.45 (1+4.5%) 30 (1+4.5%) 30

= 733+267

= $ 1000

However, when the market’s nominal annual required rate of return for both bond

issues suddenly fell from 9 percent to 8 percent r d = 8%/2 = 4%. It means Coupon rate

(4.5%) > r d (4%), so both bonds sell at a premium. Because every bond feature of Red

brewery’s bond is the same as Blue bond, except that Blue’ bonds mature in exactly 15

years, and Red’ bonds mature in 5 years (with interest paid semiannually) n Red = 10 <

n Blue = 30. Thus, Blue brewery’s bonds would show the greatest price change.

b. At the market’s new, lower required rate of return for these bonds, determine the

per bond price for each brewery’s bonds. Which bond’s price increased the most, and by

how much?

Bond price for Red brewery’s bonds at lower required rate of return with interest

paid semiannually (8%/2=4%):

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Individual Assignment Subject: Corporate Finance

VB Red = INT (1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 45 x (1+0.4) 10 -1 + 1000

4% (1+4%) 10 (1+4%) 10

= $ 1041

Bond price for Blue brewery’s bonds at lower required rate of return with interest

paid semiannually (8%/2 = 4%):

VB Blue = INT(1 + rd)n - 1

+M

rd (1 + rd)n (1 + rd)n

= 45 x (1+4 %) 30 -1 + 1000

4% (1+4%) 30 (1+4%) 30

= $ 1086

From this analysis above, it is clearly that Blue brewery’s bonds would show the

greatest price change and its bond’s price increased the most ($1086-$1000=$86).

5. Summer Stone is analyzing and investment. The expected one-year return on

the investment is 20%. The probability distribution of possible returns is

approximately normal with a standard deviation of 15%. (20 marks)

a. What are the chances the investment will result in a negative return?

Mean = 20%.

Standard deviation = 15%

Result in a negative return=> x<0%

P (x<0%) = NORM.DIST (0, 0.2, 0.15, TRUE)

Use NORMAL.DIST in excel P (x<0%) = 9.12%

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Individual Assignment Subject: Corporate Finance

b. What is the probability that the return will be greater than 10%? 50%?

- x<10%

P (x<10%) = NORM.DIST (0.1, 0.2, 0.15, TRUE) = 25.25%

P (x>10%)=100%-25.25% = 74.75%

- x<50%

P (x<50%) = NORM.DIST (0.5, 0.2, 0.15, TRUE) = 97.72%

P (x>50%)=100%-36.9% = 2.28%

6. Barnaby Company has current assets of $800’000 and current liabilities of

$500’000. What effect would the following transactions have on the firm’s current

ratio (and state the resulting figures)? (20 marks)

current assets of $800’000

current liabilities of $500’000

Current ratio =Current assets

Current liabilities

Assets = 800000 = 1.6

Current Liabilities 500000

a. Two new trucks are purchased for a total of $100’000 in cash.

Current assets $ 800’000- $100’000= $700’000

Fixed assets $100’000

current liabilities $500’000

700’000

Current ratio = = 1.4.

500’000

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Individual Assignment Subject: Corporate Finance

After Barnaby Company purchased two new trucks, current assets decreased

because of the decrease of cash, current liabilities did not change. Firm’s current ratio

decreased. However, the current ratio still > 1. This means company’s ability to pay

short-term liabilities is high.

b. The company borrows $100’000 short term to carry an increase in receivables of

the same amount.

current assets $800’000+$100’000=$900’000

current liabilities $500’000 + $100’000 = $ 600’000

800’000

New Current ratio = = 1.5.

600’000

After Barnaby Company borrows $100’000 short term to carry an increase in

receivables of the same amount, current assets increased because of the increase of AR

and current Liabilities increased due to the increase of accts. Payable. The firm’s current

ratio decreased. However, the current ratio still > 1. This means company’s ability to pay

short-term liabilities is high.

c. Additional common stock of $200’000 is sold and the proceeds invested in the

expansion of several terminals.

current assets $800’000

Fixed assets $200'000

Liabilities and equity

Current liabilities $500’000

Common stock $ 200'000

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Individual Assignment Subject: Corporate Finance

800’000

Current ratio = = 1.6.

500’000

After Barnaby Company sold common stock of $200’000 and the proceeds invested

in the expansion of several terminals, current assets did not change, and fixed assets

increased of $ 200’000 because of the expansion of several terminals. Current Liabilities

did not change. The firm’s current ratio was the same at before. The company’s ability to

pay short-term liabilities is high.

d. The company increases its account payable to pay a cash dividend of $40’000 out

of cash.

Current assets $800’000

Current liabilities $500’000

Accts payable $ 40'000

Total Current liabilities = $500’000+$40’000 = $ 540’000

Equity ($-40’000)

800’000

Current ratio = = 1.48.

540’000

After Barnaby Company increases its account payable to pay a cash dividend of

$40’000 out of cash, Current assets did not change. Current Liabilities increased due to

the increase of account payable. The firm’s current ratio decreased. However, the current

ratio still > 1. This means company’s ability to pay short-term liabilities is still high.

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