Question

Airnova Inc. has two types of bonds, Bond D and Bond F. Both have 8 percent coupons, make semiannual payments, and are priced at par value. Bond D has 2 years to maturity. Bond F has 15 years to maturity.

Airnova Inc. is considering four different types of stocks. They each have a required return of 20 percent and a dividend of $3.75 for share. Stocks, A, B, and C are expected to maintain constant growth rates in dividends for the near future of 10 percent, 0 percent, and -5 percent, respectively. Stock D is a growth stock and will increase its dividend by 30 percent for the next four years and then maintain a constant 12 percent growth rate after that

Discuss

If interest rates suddenly rise by 2 percent, what is the percentage change in both bonds?

If interest rates suddenly fall by 2 percent, what is the percentage change in both bonds?

What does this tell you about the interest rate risk of longer-term bonds?

What is the dividend yield for each of the four stocks?

What is the expected capital gains yield?

Discuss the relationship among the various returns that you find for each of the stocks.

Answer 1

Bond Coupon Rate = 8% payable semi-annually, Market Value = Par Value. Bond's Promised Yield = 8 % per annum, Bond D Tenure = 2 years or 4 half-years, Bond F Tenure = 15 years or 30 half-years.

Bond D Modified Duration = 1.81 and Bond F Modified Duration = 8.65

When Yield rises (interest rates) rise by 2 percentage points:

% Change in Bond Price = - Modified Duration x Yield Change in Basis Points

% Change in Bond D Price = - 1.81 x 200 = - 362 bps or -3.62 % approximately

% Change in Bond F Price = - 8.65 x 200 = - 1730 bps or - 17.32 % approximately

When Yield (interest rates) fall by 2 percentage points:

% Change in Bond D Price = - 1.81 x - 200 = 362 bps or 3.62 % approximately

% Change in Bond F Price = - 8.65 x - 200 = 1730 bps or 17.32 % approximately

As is observable the longer maturity bond (Bond F) is more sensitive to equal alterations in interest rates as compared to the shorter maturity bond. Hence, a longer maturity bond has a higher interest rate risk as compared to a shorter maturity bond.

Stock A:

Required Return = r = 20%. Last Dividend = $ 3.75 and Dividend Growth Rate = g = 10 %

D1 = 3.75 x 1.1 = $ 4.125

Stock Price = P0 = D1 / (r - g) = 4.125 / (0.2 - 0.1) = $ 41.25

Dividend Yield = D1 / P0 = 4.125 / 41,25 = 0.1 or 10 %

Stock B:

Required Return = r = 20%. Last Dividend = $ 3.75 and Dividend Growth Rate = g = 0 %

D1 = 3.75 x 1 = $ 3.75

Stock Price = P0 = D1 / (r - g) = 3.75 / (0.2 - 0) = $ 18.75

Dividend Yield = D1 / P0 = 3.75 / 18.75 = 0.2 or 20 %

Stock C:

Required Return = r = 20%. Last Dividend = $ 3.75 and Dividend Growth Rate = g = - 5 %

D1 = 3.75 x 0.95 = $ 3.5625

Stock Price = P0 = D1 / (r - g) = 3.5625 / (0.2 - (-0.05)) = $ 14.25

Dividend Yield = D1 / P0 = 3.5625 / 14.25 = 0.25 or 25 %

Stock D:

Required Return = r = 20%. Last Dividend = $ 3.75 and Dividend Growth Rate = g = 30 % for the first four years followed by a perpetual constant growth of 12 % per annum.

D1 = 3.75 x 1.3 = $ 4.875, D2 = 4.875 x 1.3 = $ 6.3375, D3 = 6.3375 x 1.3 = $ 8.23875, D4 = 1.3 x 8.23875 = $ 10.710375

Terminal Value (TV) of perpetually growing dividends at end of Year 4 = (10.710375 x 1.12) / (0.2 - 0.12) = $ 149.945

PV of TV of perpetually growing dividends = P1 = 149.945 / (1.2)^(4) = $ 72.31

PV of supernormally growing dividend stream = P2 = 4.875 / 1.2 + 6.3375 / (1.2)^(2) + 8.23875 / (1.2)^(3) + 10.710375 / (1.2)^(4) = $ 18.396

Stock Price = P0 = P1 + P2 = 149.945 + 18.396 = $ 168.34

Dividend Yield = D1 / P0 = 4.875 / 168.34 = 0.0289 or 2.89 %

NOTE: Please raise separate queries for solutions to the remaining sub-parts.