Question

There is a corporate bond with 5-year maturity. Its par value is $1000. Its coupon is paid semiannually with $5 each time. And the stock price of this firm is $50 per share now. The share outstanding is 20,000 shares. Suppose this firm keeps paying dividends annually. And the dividend is growing each year. And shareholders got $2 as the dividend per share for this year. The firm's Return of Equity is 0.06. Its Plowback Ratio is 0.4. The inflation rate is 2%. The nominal interest rate is 5%. All interest rates are compound interest rates.

a. What are the present values of the bond and the stock?

b. What is the Present Value of Growth Opportunities for the stock?

c. Suppose I bought this bond at the beginning. What is the Yield to Maturity and the Internal Rate of Return of the bond if I sell this bond at the end of the third year with the price of $ 944?

Answer 1

a) (i)Present value of bond:

Par value = $1,000 ; Time to Maturity = 5 years; Coupon = $5 Semiannually ; Discounting factor (r) = nomical interest rate + inflation rate = 5% + 2% = 7%

Therefore with all the given information lets find the present value of bond = 5*[(1 - (1/((1+r)^n))/r] + 1,000/(1+r)^n

= 5*[(1 - (1/((1+0.07/2)^(5*2)))/(0.07/2)] + 1,000/(1+(0.07/2))^(5*2)

= $41.58 + $708.92 = $750.50 (aprrox)

(ii)Present value of share:

Growth rate of the earnings = Plowback ratio * ROE = 40%*6% = 2.4%

Present value of dividend = $2/share

Therefore using the Dividend Disount Model = PV of Share = Dividend₁/(Ke - g)

= 2(1.024)/(0.07 - 0.024) = $44.52 {Assuming the Cost of Equity be equal to the market real interest rate, 7%}

b) PV of Growth Oppertunity can be defined as the analysing the equity share as the combinationation of the fundamental and expectation from the investor for the future growth oppertunity.

PVGO = Value of stock - Value of no growth

{Note: Value of no growth means if there's is no positive NPV projects available to invest, value we found earlier in a(ii) part of $44.52}

= $50 - $44.52 = $5.48

c) (i)YTM calculation:

Current Bond price = $944 at the end of third year, means remaining years = 2 years at discounting factor = 7%

Using the estimation method = YTM= ( Coupon + (Face value + Price)/n) / ((Face value + Price)/2)

= ( 5 + (944 - 750.50)/(3*2)) / ((944 + 750.50)/2) {Face value we have taken as $944 as the bond is sold and we are finding the YTM till the date it was sold}

Solving above equation we get,

= 0.043849 or 4.38% (approx)

(ii) IRR calculation:

Year	Cash Flows
0	-$750.5
0.5	$5
1	$5
1.5	$5
2	$5
2.5	$5
3	$5 + $944
IRR	4.50%