Question

Assume that an investor pays $920 for a​ long-term bond that carries a coupon of 6%. In 3​ years, he hopes to sell the issue for ​$1,070. If his expectations come​ true, what yield will this investor​ realize? (Use annual​ compounding.) What would the holding period return be if he were able to sell the bond​ (at $1,070) after only 9​ months?

The yield will be __ % (Round to two decimal​ places.)

The holding period return will be __ % (Round to two decimal​ places.)

Answer 1

part a) The yield will be 11.38%

Appropriate yield = {Coupon+[(selling price-purchase price)/n]}/{(selling price+purchase price)/2}

where, Assume face value = $1,000 coupon = face value*coupon rate = $1,000*6% = $60 selling price = $1,070 Purchase price =$920 n = 3years

Appropriate yield = {60+[(1070-920)/3]}/{(1070+920)/2} = {60+(150/3)}/(1990/2) = (60+50)/995 = 110/995 = 11.06%

Computation using discounted cashflow method:

Year	Type	Cashflow	PVF @ 11%	Discounted cashflow @ 11% (cashflow * PVF @ 11%)	PVF @ 11.5%	Discounted cashflow @ 11.5% (cashflow * PVF @ 11.5%)
1	Coupon	60	1/(1+Discount rate) = 1/(1.11) = 0.9009	54.05	1/(1+Discount rate) = 1/(1.115) = 0.8969	53.81
2	Coupon	60	1/[(1+Discount rate)^2] = 1/[(1.11)^2] = 0.8116	48.70	1/[(1+Discount rate)^2] = 1/[(1.115)^2] = 0.8044	48.26
3	Coupon	60	1/[(1+Discount rate)^3] = 1/[(1.11)^3] = 0.7312	43.87	1/[(1+Discount rate)^3] = 1/[(1.115)^3] = 0.7214	43.28
3	Sale	1,070	1/[(1+Discount rate)^3] = 1/[(1.11)^3] = 0.7312	782.38	1/[(1+Discount rate)^3] = 1/[(1.115)^3] = 0.7214	771.90
				929.01		917.26

Yield = Base rate + (Σ Discounted cashflow @ 11%-purchase price)*difference in discount rate/(Σ Discounted cashflow @ 11%-Σ Discounted cashflow @ 11.5%) = 11% + (929.01-920)*(11.5%-11%)/(929.01-917.26) = 11% + (9.01*0.5%/11.75) = 11% + 0.38% = 11.38%

Part b) Holding period yield = 73.43%

He is able to sell after only 9 months means after 9months from purchase date he can able to sell @ $1,070

Future value = present value*[(1+r)^n]

1070 = 920*[(1+r)^(9/12)]

(1+r)^0.75 = 1070/920

(1+r)^0.75 = 1.163043

(1+r)^0.75 = (1.550725)^0.75

r = 1.550725-1

r = 0.550725 or 55.07%

Annualised rate = r*12months/9months = 55.07%*12/9 = 73.43%