Explore BrainMass

# Bond Values and Stock Prices

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Part a

Assume you hold a corporate bond with a \$1,000 par value paying a 7 &#8541; 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.

© BrainMass Inc. brainmass.com October 6, 2022, 9:04 am ad1c9bdddf
https://brainmass.com/economics/bonds/bond-values-stock-prices-18683

## SOLUTION This solution is FREE courtesy of BrainMass!

See attached file

Bond Values and Stock Prices
Part a

Assume you hold a corporate bond with a \$1,000 par value paying a 7 &#8541; 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

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%