Question

5.  Neptune Mining (NM) has two outstanding bonds:

Bond 1:  Par Value = $200 million; Coupon Rate = 3.1%; Yield to Maturity = 4.2%; Maturity Date = 40 years

Bond 2:  Par Value = $300 million; Coupon Rate during Years 1-8 = 4.3%; Coupon Rate during Years 9-10 = 4.8%; Yield to Maturity = 4.1%

Details on NM equity shares:

Current Dividend = $1.58; Growth Rate in Dividends = 2.83%; Required return = 9.61%

A.  Compute the price of both bonds.

B.  Compute the price of the stock using the Gordon growth model.

C.  Compute the sinking fund payment for Bond 1 if the return provided by the financial institution is 4.2% and the payments begin exactly 15 years before the bond matures.

Answer 1

A. Prices of bonds.
Bond 1:

	Bond 1	Calculation
Future Value	200000000	Given
Coupon	6200000	3.1%*200000000
YTM	4.20%	Given
Time to maturity	40	Given
Periodicity	Annual	Given
Price	15,77,22,379.80	Financial Calculator

N = 40
PMT = 6200000
FV = 200000000
I/Y = 4.2
CPT PV = 157722379.8

Excel can also be used:

Year	Cash Flow	Discounting Factor	Present Value
0	0	1	0
1	6200000	0.959692898	5950095.97
2	6200000	0.921010459	5710264.85
3	6200000	0.883887197	5480100.62
4	6200000	0.848260266	5259213.65
5	6200000	0.814069353	5047229.99
6	6200000	0.781256577	4843790.77
7	6200000	0.749766388	4648551.61
8	6200000	0.719545478	4461181.96
9	6200000	0.690542685	4281364.65
10	6200000	0.662708911	4108795.25
11	6200000	0.635997036	3943181.62
12	6200000	0.610361838	3784243.4
13	6200000	0.585759922	3631711.51
14	6200000	0.562149637	3485327.75
15	6200000	0.539491014	3344844.29
16	6200000	0.517745695	3210023.31
17	6200000	0.496876867	3080636.57
18	6200000	0.4768492	2956465.04
19	6200000	0.457628791	2837298.5
20	6200000	0.439183101	2722935.23
21	6200000	0.421480903	2613181.6
22	6200000	0.404492229	2507851.82
23	6200000	0.38818832	2406767.58
24	6200000	0.372541574	2309757.76
25	6200000	0.357525503	2216658.12
26	6200000	0.343114686	2127311.05
27	6200000	0.329284727	2041565.31
28	6200000	0.316012214	1959275.73
29	6200000	0.303274678	1880303
30	6200000	0.291050555	1804513.44
31	6200000	0.27931915	1731778.73
32	6200000	0.268060605	1661975.75
33	6200000	0.257255859	1594986.32
34	6200000	0.246886621	1530697.05
35	6200000	0.236935337	1468999.09
36	6200000	0.22738516	1409787.99
37	6200000	0.218219923	1352963.52
38	6200000	0.20942411	1298429.48
39	6200000	0.200982832	1246093.56
40	206200000	0.192881796	39772226.4
		Bond Price	157722380

Bond 2:

	Bond 1	Calculation
Future Value	30,00,00,000.00	Given
Coupon 1-8	1,29,00,000.00	4.3%*300000000
Coupon 8-10	1,44,00,000.00	4.8%*300000000
YTM	4.10%	Given
Time to maturity	10	Given
Periodicity	Annual	Given
Price	10,61,60,084.62	Financial Calculator

Excel:

Year	Cash Flow	Discounting Factor	Present Value
0	0	1	0
1	1,29,00,000.00	0.960614793	12391930.8
2	1,29,00,000.00	0.922780781	11903872.1
3	1,29,00,000.00	0.88643687	11435035.6
4	1,29,00,000.00	0.851524371	10984664.4
5	1,29,00,000.00	0.817986907	10552031.1
6	1,29,00,000.00	0.785770324	10136437.2
7	1,29,00,000.00	0.754822598	9737211.51
8	1,29,00,000.00	0.725093754	9353709.42
9	1,44,00,000.00	0.696535786	10030115.3
10	1,44,00,000.00	0.669102581	9635077.16
		Price	106160085

B. Price of stock

Dividend	1.58
Growth rate	2.83%
Rate of return	9.61%
Stock price	23.96333333

Formula:
[ D₀*(1+g) ] / (r - g)

where D0 is the current dividend
g = growth rate
r = rate of return

C. Annual payment to Sinking Fund:

Redemption	206200000
Time to Maturity	15
Rate	4.20%
Annual Sinking Fund payment	(1,01,45,747.70)

PMT function of excel was used.
=PMT(4.2%,15,,206200000)

Using a financial calculator:

I/Y = 4.2%
N = 15
FV = 206200000
CPT PMT = 10145747.7