Question

Today is 1 July 2020. Joan has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Joan purchased all instruments on 1 July 2012 to create this portfolio and this portfolio is composed of 28 units of instrument A and 50 units of instrument B.

Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 January 2030.

Instrument B is a Treasury bond with a coupon rate ofj₂ = 3.93% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(b) Calculate the current price of instrument B per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ = 2.96% p.a. and Joan has just received the coupon payment.

Select one:

a. 104.2859

b. 102.3209

c. 108.6995

d. 102.7650

Answer 1

On excel Use PV function

PV(rate,nper,PMT,-FV)

=PV(2.96%/2,2*2.5,-1.965,-100)

=102.3209

Correct option is B

However its important to understand the question

whenever there are semi annual payments

interest is divided by 2

time is multiplied by 2

Step1=Rate.

Yield rate given is

j2=2.96%p.a since it is semi annual hence divided by 2

Step2=NPER

Time period=bond is maturing in 2023

since question says JOAN just received the payment hence

Time period left =2.5 years

due to semi annual time will be doubled=2.5*2

Step3

PMT

this is the payment on treasury bond hence

(3.93%*100)/2=1.965

Step4

Future value =100