# Bond Values and Stock Prices

Part a

Assume you hold a corporate bond with a $1,000 par value paying a 7 ⅝ coupon rate that has two years left until maturity. Calculate the value of the bond if the current market interest rate on a bond of this risk is 9 %.

Part b

Assume that you hold a share of common stock that will pay a dividend of $5.00 per share for the next three years. At the end of the third year, you expect the price per share to be $50. Calculate the value of the stock if your required rate of return is 11 %.

Part c

Calculate the price of a share of stock that is expected to pay a $15 dividend in perpetuity if the stock is priced to yield an 11.5% rate of return.

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Bond Values and Stock Prices

Part a

Assume you hold a corporate bond with a $1,000 par value paying a 7 ⅝ coupon rate that has two years left until maturity. Calculate the value of the bond if the current market interest rate on a bond of this risk is 9 %.

7 5/8 = 7.625%

Discount rate= 9.000%

We assume that the bond pays semi annual interest

To calculate the price of the bond we need to calculate / read from tables the values of

PVIF= Present Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity

Price of bond= PVIF * Redemption value + PVIFA * interest payment

Price of bond

Coupon rate= 7.625%

Face value= 1000

Payment S Semi Annual

No of years= 2

No of Periods= 4

Discount rate annually= 9.00% annual

Discount rate per period= 4.50%

n= 4

r= 4.50%

Interest payment= 38.125 Semi Annual =(7.625%/2)*1000

Redemption value= 1000

PVIF 4 periods, 4.5% rate= 0.8386

PVIFA 4 periods, 4.5% rate= 3.5875

Price of bond=PVIFA X Interest Payment+PVIF X Redemption value

PVIFA X Interest Payment= 136.77 =3.5875*38.125

PVIF X Redemption value= 838.6 =0.8386*1000

Total 975.37 =Price of bond

The price of the bond= $975.37

Answer:Value of the bond= $975.37

There is an alternative way of solving the problem

We discount the cash flows

Discount rate= 9.00% Annual

No of periods Cash flow Present value factor at 4.5%= 1/(1+4.5%)^no of periods Discounted cash flow

Coupon Principal Total

1 38.125 38.125 0.9569 36.482 =38.125*0.9569

2 38.125 38.125 0.9157 34.911 =38.125*0.9157

3 38.125 38.125 0.8763 33.409 =38.125*0.8763

4 38.125 1000 1038.125 0.8386 870.572 =1038.125*0.8386

$975.37

Price of bond= $975.37

If instead we assume that interest payments are annual

Price of bond

Coupon rate= 7.625%

Face value= 1000

Payment A Annual

No of years= 2

No of Periods= 2

Discount rate annually= 9.00% annual

Discount rate per period= 9.00%

n= 2

r= 9.00%

Interest payment= 76.25 Annual =7.625%*1000

Redemption value= 1000

PVIF 2 periods, 9.% rate= 0.8417

PVIFA 2 periods, 9.% rate= 1.7591

Price of bond=PVIFA X Interest Payment+PVIF X Redemption value

PVIFA X Interest Payment= 134.13 =1.7591*76.25

PVIF X Redemption value= 841.7 =0.8417*1000

Total 975.83 =Price of bond

The price of the bond= $975.83

Answer:Value of the bond= $975.83

There is an alternative way of solving the problem

We discount the cash flows

Discount rate= 9.00% Annual

No of periods Cash flow Present value factor at 9% = 1/(1+9%)^no of periods Discounted cash flow

Coupon Principal Total

1 76.25 76.25 0.9174 69.952 =76.25*0.9174

2 76.25 1000 1076.25 0.8417 905.88 =1076.25*0.8417

$975.83

Price of bond= $975.83

Part b

Assume that you hold a share of common stock that will pay a dividend of $5.00 per share for the next three years. At the end of the third year, you expect the price per share to be $50. Calculate the value of the stock if your required rate of return is 11 %.

We will discount ( at the required rate of return= 11 %)the dividends and the price of the bond that we will receive at the end of 3 years

Year Cash flow Present value factor at 11 %= 1/(1+11%)^no of years Discounted cash flow

Dividend Price of share Total

1 5 5 0.9009 4.505 =5*0.9009

2 5 5 0.8116 4.058 =5*0.8116

3 5 50 55 0.7312 40.216 =55*0.7312

$48.78

Value of stock= $48.78

Answer: $48.78

Part c

Calculate the price of a share of stock that is expected to pay a $15 dividend in perpetuity if the stock is priced to yield an 11.5% rate of return.

Price of share= Po= Div/ r

Div=Perpetual dividend $15

r=required rate of return= 11.50%

Po= Div/ r= $130.43 =15/11.5%

Answer: $130.43

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