Question

What is the price of a 4​-year, 7.8% coupon​ rate, $1,000 face value bond that pays interest annually if the yield to maturity on similar bonds is 6.7%​?

Answer 1

Sol:

Face value (FV) = $1000

Period (n) = 4 years

Coupon rate = 7.8%, Annual coupon payment = 1000 x 7.8% = 78

Yield to maturity (r) = 6.7%

To determine Present value (PV) of the bond:

Present value (PV) = (PMT x (1-(1+r)^-n)/r) + (FV/(1+r)^n)

PV = 78 x (1-(1 + 6.7%)^-4) / 6.7% + (1000 / (1 + 6.7%)^4

PV = 78 x (1-(1.067)^-4) / 0.67 + (1000 / (1.067)^4

PV = 78 x (1-(1.067)^-4) / 0.067 + (1000 / (1.067)^4

PV = 266.0017 + 771.5114

PV = $1037.51

Therefore Price of the bond will be $1037.51

Present value (PV) of the bond, we can use PV function in excel sheet:

FV	1000
PMT	78
NPER	4
Yield	6.70%
PV	$1,037.51

Working

A B 1 FV 1000 2 PMT 78 3 NPER 4 4 Yield 0.067 5 PV =PV(B4,B3,B2,B1,0) *-1