Question

Consider

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

1-	AT 5% YTM price of Bonds =10/2 =5%
	Value of Bond D	(coupon payment*PVAF at 5% for 4 semi annual period)+(face value*pvf at 5% at 4th semiannual period)	(40*3.5458)+(1000*.8227)		964.532
	PVAF at 5% for 4 semi annual period	1-(1+r)^-n/ r	1-(1.05)^-4 / 5%	.17729/5%	3.5458
	PVF at 5% at 4th semi annual period	1/(1+r)^n	1/(1.05)^4		0.82270247
	Value of Bond F	(coupon payment*PVAF at 5% for 4 semi annual period)+(face value*pvf at 5% at 4th semiannual period)	(40*15.3724)+(1000*.2313)		846.196
	PVAF at 5% for 30 semi annual period	1-(1+r)^-n/ r	1-(1.05)^-30 / 5%	.76862/5%	15.3724
	PVF at 5% at 30th semi annual period	1/(1+r)^n	1/(1.05)^30		0.23137745
	% change in value of Bond D	(new price-old price)/old price	(964.53-1000)/1000	-3.55%
	% change in value of Bond F	(new price-old price)/old price	(846.19-1000)/1000	-15.38%
2	AT 3% YTM price of Bonds = 6/2 = 3%
	Value of Bond D	(coupon payment*PVAF at 4% for 4 semi annual period)+(face value*pvf at 4% at 4th semiannual period)	(40*3.7170)+(1000*.8227)		1030.232
	PVAF at 3% for 4 semi annual period	1-(1+r)^-n/ r	1-(1.03)^-4 / 3%	.17729/5%	3.5458
	PVF at 3% at 4th semi annual period	1/(1+r)^n	1/(1.03)^4		0.88848705
	Value of Bond F	(coupon payment*PVAF at 3% for 4 semi annual period)+(face value*pvf at 3% at 4th semiannual period)	(40*19.6003)+(1000*.2313)		1015.312
	PVAF at 3% for 30 semi annual period	1-(1+r)^-n/ r	1-(1.03)^-30 / 5%	.58801/3%	19.6003333
	PVF at 3% at 30th semi annual period	1/(1+r)^n	1/(1.03)^30		0.23137745
	% change in value of Bond D	(new price-old price)/old price	(1030.23-1000)/1000	3.02%
	% change in value of Bond F	(new price-old price)/old price	(1015.31-1000)/1000	1.53%
3-	From the above analysis it can be concluded that Bonds with higher maturity are more exposed to interest rate risk in comparison to short term maturity bonds.
4-	Price of Stock A	(expected dividend)/(required rate of return-growth rate)	(3.75*1.1)/(20%-10%)	41.25
	Price of Stock B	(expected dividend)/(required rate of return-growth rate)	(3.75*1.0)/(20%-0%)	18.75
	Price of Stock C	(expected dividend)/(required rate of return-growth rate)	(3.75*.95)/(20%--5%)	14.25
	Price of Stock D
	Year
	0	3.75
	1	3.75*1.3^1	4.875
	2	3.75*1.3^2	6.3375
	3	3.75*1.3^3	8.23875
	4	3.75*1.3^4	10.710375
	5	10.7103*1.12	11.995536
	terminal value =expected dividend in year 5/(required return-growth rate)	(11.99)/(20%-12%)	149.875
	Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =20% n =1,2,3….4
	1	4.875	4.0625
	2	6.3375	5.28125
	3	8.23875	4.76779514
	4	10.710375	5.1651114
	4	149.875	72.2776813
	value of bond D = sum of present value of cash flow		91.55
4-	Dividend Yield on shares	dividend declared	Share price	Dividend Yield = dividend paid/price of stock
	Shares
	A	3.75	41.25	9.09%
	B	3.75	18.75	20.00%
	C	3.75	14.25	26.32%
	D	3.75	91.55	4.10%
	Capital Gain Yield = stock price at the end of next year/stock price today
	stock price at the end of next year-A = dividend declared*(1+growth rate)^2 / (required rate-growth rate)	(3.75*1.1^2)/(20%-10%)	45.375
	stock price at the end of next year-B = dividend declared*(1+growth rate)^2 / (required rate-growth rate)	(3.75*1.0^2)/(20%-0%)	18.75
	stock price at the end of next year-A = dividend declared*(1+growth rate)^2 / (required rate-growth rate)	(3.75*.95^2)/(20%--5%)	13.54
	stock price at the end of next year-D = dividend declared*(1+growth rate)^2 / (required rate-growth rate)	(6.33)/1.2^1 +(103.95/1.2^1	91.9
	Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =20% n =1,2,3….4
	1	6.3375	5.28125
	2	8.23875	5.72135417
	3	10.710375	6.19813368
	3	149.875	86.7332176
	value of bond D = sum of present value of cash flow		103.933955
5-	Capital gain yield
	Stock	stock price after a year	stock price today	Capital gain yield = (stock price after a year/stock price today)-1
	A	45.375	41.25	10.0%
	B	18.75	18.75	0.00%
	C	13.54	14.25	-5.00%
	D	91.9	91.5543379	0.38%