Question

 

Suppose the discount rate is 8%. You bought a 12% coupon bond with 5 years left until maturity. After holding it for 3 years, the discount rate changed to 5% and sold the bond right after the discount rate change. What is your HPR?

Answer 1

Calculation of purchase price of the bond;

Annual coupon amount = $1000 * 0.12 = $120

Maturity value = $1000

Discount rate = 0.08

Maturity period = 5 years

 

Year	Cash flow	Discount factor @8%	Present value
Y	C	D=1/(1+discount rate)^Y	PV = (C*D)
1	120	0.925925925926	111.1111111
2	120	0.857338820302	102.8806584
3	120	0.793832241020	95.25986892
4	120	0.735029852796	88.20358234
5	120	0.680583197034	81.66998364
5	1000	0.680583197034	680.583197
		Purchase price	$ 1,159.7084

 

Purchase price of the bond = $1,159.7084 

 

Calculation of sales price of the bond;

Annual coupon amount = $1000 * 0.12 = $120

Maturity value = $1000

Discount rate = 0.05

Maturity period = 2 years (i.e. 5 years - 3 years)

Year	Cash flow	Discount factor @5%	Present value
Y	C	D=1/(1+discount rate)^Y	PV = (C*D)
1	120	0.952380952381	114.2857143
2	120	0.907029478458	108.8435374
2	1000	0.907029478458	907.0294785
		Sales price	$ 1,130.1587

 

Sales price of the bond = $1,130.1587

 

Calculation of holding period return (HPR);

 

Formula;

HPR = [Coupon received + (Sales price - Purchase price)] / Purchase price * 100

HPR = [($120 * 3) + ($1,130.1587 - $1,159.7084)] / $1,159.7084 * 100

HPR = ($360 - 29.5497) / $11.597084

HPR = $330.4503 / $11.597084

 

HPR = 28.4943% or 28.49% (Approx.)

HPR = 28.4943% or 28.49% (Approx.)