Question

1....Madison Corporation has a $1,000 par value bond outstanding with a coupon rate of 9% interest. Interest payments are made semiannually. The bond matures in 20 years. If the yield to maturity for similar bonds is 9%, what is the value of the bond? Select one: A. $1,644 B. $1,000 C. $935 D. $908

2....What is the yield to maturity for $1,000 par value bond that pays a coupon rate of interest of 11%, has seven years to maturity, and is currently selling for $952?

Select one:

A. 10.52%

B. 11.63%

3....

A 30-year zero-coupon bond that yields 11% percent per year is issued with a $1,000 par value. What is the price of the bond on its date of issue?

Select one:

A. $33.38

B. $43.68

C. $98.43

D. $54.89

C. 12.05%

D. 13.12%

4.

A share of common stock has just paid an annual dividend of $4.00. The dividend growth rate is expected to be 8%. If the required rate of return is 12%, what is the current price per share?

Select one:

A. $100

B. $80

C. $86.40

D. None of these answers are correct

Answer 1

1)Givenn interest rate = 9%

Coupon Amount = $ 1000*9%= $ 45 ( Since Coupons are paid semi annually)

YTM = 9%

YTM for 6 months= 9%/2=4.5%

Computation of value of the bond:

S.No	Cash flow	Disc @ 4.5%	Discounted Cash flows
1	$45	0.9569	$43.06
2	$45	0.9157	$41.21
3	$45	0.8763	$39.43
4	$45	0.8386	$37.74
5	$45	0.8025	$36.11
6	$45	0.7679	$34.56
7	$45	0.7348	$33.07
8	$45	0.7032	$31.64
9	$45	0.6729	$30.28
10	$45	0.6439	$28.98
11	$45	0.6162	$27.73
12	$45	0.5897	$26.53
13	$45	0.5643	$25.39
14	$45	0.5400	$24.30
15	$45	0.5167	$23.25
16	$45	0.4945	$22.25
17	$45	0.4732	$21.29
18	$45	0.4528	$20.38
19	$45	0.4333	$19.50
20	$45	0.4146	$18.66
21	$45	0.3968	$17.86
22	$45	0.3797	$17.09
23	$45	0.3634	$16.35
24	$45	0.3477	$15.65
25	$45	0.3327	$14.97
26	$45	0.3184	$14.33
27	$45	0.3047	$13.71
28	$45	0.2916	$13.12
29	$45	0.2790	$12.56
30	$45	0.2670	$12.02
31	$45	0.2555	$11.50
32	$45	0.2445	$11.00
33	$45	0.2340	$10.53
34	$45	0.2239	$10.08
35	$45	0.2143	$9.64
36	$45	0.2050	$9.23
37	$45	0.1962	$8.83
38	$45	0.1878	$8.45
39	$45	0.1797	$8.08
40	$1,045	0.1719	$179.67
	Total		$1,000.00

So the value of the bond is $ 1000

Hence option B) $ 1000 is the Correct answer.

2) Computation of YTM of a bond

Year	Cash flow	Disc @ 10.52%	DCF	Disc @ 11.63%	DCF	Disc @ 12.05%	Disc	Disc@ 13.12%	DCF
1.0000	110.0000	0.9048	99.5295	0.8958	98.5398	0.8925	98.1705	0.8840	97.2419
2.0000	110.0000	0.8187	90.0556	0.8025	88.2736	0.7965	87.6131	0.7815	85.9635
3.0000	110.0000	0.7408	81.4836	0.7189	79.0770	0.7108	78.1911	0.6908	75.9932
4.0000	110.0000	0.6702	73.7274	0.6440	70.8384	0.6344	69.7823	0.6107	67.1792
5.0000	110.0000	0.6065	66.7096	0.5769	63.4582	0.5662	62.2778	0.5399	59.3876
6.0000	110.0000	0.5487	60.3597	0.5168	56.8469	0.5053	55.5804	0.4773	52.4996
7.0000	1110.0000	0.4965	551.1082	0.4629	513.8738	0.4509	500.5413	0.4219	468.3249
		Total	1022.9737		970.9078		952.1564		906.5898

Interest amount = $ 1000*11% = $ 110

We know that at YTM of the bond, Present value of the future cash flows = market price

Since the above condition satisfies when YTM is 12.05%

So Option C) 12.05% is the correct answer.

3)For a Zero Coupon bond, there is a single cash flow occur at the end of the maturity period

YTM = 11%

Term to Maturity (n)= 30 years

Present value of the bond = Future value /( 1+i)^n

Here I = interest rate.

Future value = $ 1000

Present value of the bond = $ 1000/(1+11%)^30

= $ 1000/(1.11)^30

= $ 1000/22.89229657

= $43.68281

So the present value of the bond is $ 43.68

Hence option B) $ 43.68 is the correct answer.

4)Paid Annual Dividend = $ 4

Expected Annual Dividend(D1) = $ 4+$ 4*8/100

= $ 4.32

We know that Value of the dividend growing stock as on today is D1/(r-g)

r= Rate of interest

g= Growth rate

Given r= 12% , g=8%

Current market price = D1/(r-g)

=$ 4.32/(0.12-0.08)

= $ 4.32/$ 0.04=$ 108

So the Current Market price per share is $ 108

Hence Opttion D) None of the answers are correct.