Question

a) A loan of £100 nominal is issued with interest payments (coupon) payable at 8% p.a. monthly in arrears for 7 years, with the amount of the loan repayable at the end of the term. For an investor who is not liable to income tax or capital gains tax, with a required redemption yield of 6%pa: i) Calculate the price the investor should pay for the loan. li) If the price of the loan is £100, with the same interest payments, determine the [2 marks] amount that would be needed to be paid at redemption in order to achieve the required rate of return. [1 mark] ii) If the loan is priced at £100 with a redemption payment of £110 and the same [4 marks] interest payments as above, calculate the redemption yield achieved.

Answer 1

Answer:

I)

Given

Nominal Loan Amount A=100

Coupon rate= 8%

Coupon =100**8%=8 per annum

Coupon per month C=8/12=0.67

Redemption yield=6 % p.a

Redemption yield per month r=6%/12=0.5%

Periods n=12*7=84 months

So Price of Loan=C*{1-(1+r)^-n}/r + A/(1+r)^n=0.67*(1-(1+0.5%)^-84)/0.5% + 100/(1+0.5%)^84

Price of Loan= 111.64

II)

Given

Price of Loan Amount P=100

Coupon rate= 8%

Coupon =100**8%=8 per annum

Coupon per month C=8/12=0.67

Redemption yield=6 % p.a

Redemption yield per month r=6%/12=0.5%

Periods n=12*7=84 months

Let A=Nominal loan amount at redemption

So Price of Loan P=C*{1-(1+r)^-n}/r + A/(1+r)^n

100=0.67*(1-(1+0.5%)^-84)/0.5% + A/(1+0.5%)^84

A=82.31

III)

Given

Noimnal Loan amount at redemption A=110

Price of Loan Amount P=100

Coupon rate= 8%

Coupon =100**8%=8 per annum

Coupon per month C=8/12=0.67

Let Redemption yield per month =r

Periods n=12*7=84 months

So Price of Loan P=C*{1-(1+r)^-n}/r + A/(1+r)^n

100=0.67*(1-(1+r)^-84)/r + 110/(1+r)^84

Solving for r we get r=0.756% per month

Annual Redemption yield=12*r=9.07% per annum

A=82.31