Question

2. Evaluate which of the following options would be your best investment based solely on the yield to maturity criterion. Option #1: Purchase a $60,000 coupon bond with a 7.5% coupon rate selling for $58,800 and maturing in 12 years Option #2: Purchase a $60,000 discount bond selling for $34,100 and maturing in 12 years Option #3: Loan a reliable friend $60,000 with promised repayments of $11,925.19 at the end of year 4, $28,442.01 at the end of year 8, and $50,876.44 at the end of year 12. Assume the payments represent 1/6, 2/6, and 3/6 repayment of the original loan amount respectively.

Answer 1

Answer:

Option 1 is financially better based on YTM. See calculations below.

Workings:
Yield of Maturity of Option 1:

Years	Cash Flow	Discount Factor at 5%	Present Value	DF at 8%	Present Value
0	-58800	1.0000	-58,800.00	1.0000	-58,800.00
1 to 8	4500	6.4632	29,084.46	5.7466	25,859.88
8	60000	0.67684	40,610.36	0.54027	32,416.13
			10,894.82		-523.99

IRR = YTM = 5% + (10894.82)/(10894.82+523.99) x 3 = 7.86% [A more precise calculation can result in 7.85%, that is if we take 7% and 8% to interpolate.]

Yield to Maturity of Option 2:

Years	Cash Flow	Discount Factor at 5%	Present Value	DF at 4%	Present Value
0	-34100	1.0000	-34,100.00	1.0000	-34,100.00
12	60000	0.5568	33,410.25	0.6246	37,475.82
			-689.75		3,375.82

IRR = YTM = 4% + (3375.82)/(3375.82+689.75) x 1 = 4.83%

Yield to Maturity of Option 3:

Years	Cash Flow	Discount Factor at 5%	Present Value	DF at 4%	Present Value
0	-60,000.00	1.0000	-60,000.00	1.0000	-60,000.00
4	11,925.19	0.8227	9,810.88	0.8548	10,193.70
8	28,442.01	0.6768	19,250.67	0.7307	20,782.30
12	50,876.44	0.5568	28,329.91	0.6246	31,777.27
			-2,608.54		2,753.27

IRR = YTM = 4% + (2753.27)/(2753.27+2608.54) x 1 = 4.51%

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