Question

a) The will of Warren’s grandfather provided that, starting at the end of year 1, Warren is to receive £14,000 a year forever. If Warren wants to sell the right to receive such stream of payments and the annual interest rate is 7 per cent, how much should he ask for? Now determine the value of this stream of payments if the first payment would occur starting at the end of the year 4? Explain your calculations in each case.

[5 marks]

b) Warren is about to deposit his savings of £100,000 and is considering three banks. All these banks offer a nominal annual interest rate of 12 per cent, but they all offer different compounding periods. Banks 1, 2 and 3 offer semi-annual, quarterly and monthly compounding respectively. What is the effective annual interest rate offered by each bank? Explain the difference between the nominal annual interest rate and the effective annual interest rate.

[5 marks]

c) Take the above deposits remuneration in b) and determine how much would Warren have in each deposit in Bank 1, 2 and 3 at the end of Years 1 and 5. Explain why each deposit might generate a different return.

[5 marks]

d) What is the price of a 25-year sovereign bond with a 4.5 per cent yield with annual coupons of 3.5 per cent and a £1,000 face value? How do you define a sovereign bond?

[5 marks]

e) Take the above bond in d) and determine what would be the price of this bond if it paid no coupons? How would you define this type of bond? What would be the benefits for a corporation to issue a bond with no coupons?

Answer 1

A) PV of Stream Today = 14000 / 7% = 200000

Therefore, warren would ask for $200000

First Calculate PV of Stream @ end of Year 4 = 14000 / 7% = 200000

Then Discount this back today = 200000 / (1.07) ^4 = 152579.04

This lower because we are not getting anything in year 1 to 4

B) Nominal annual interest rate = 12%

Bank 1 (Semi Annually)

Effective annual interest rate = [(1+0.12 / 2) ^ 2] -1 = 12.36%

Bank 2 (Quarterly)

Effective annual interest rate = [(1+0.12 / 4) ^ 4] -1 = 12.55%

Bank 3 (Monthly)

Effective annual interest rate = [(1+0.12 / 12) ^ 12] -1 = 12.68%

Since Effective interest rate will take into consideration the compounding effect or you can say interest on interest it is more than nominal interest rate.

C)

Bank 1 (Semi Annually)

End of Year 1 = [(1+0.1236) ^ 1] * 100000 = 112360

End of Year 5 = [(1+0.1236) ^ 5] * 100000 = 179085

Bank 2 (Quarterly)

End of Year 1 = [(1+0.1255) ^ 1] * 100000 = 112550

End of Year 5 = [(1+0.1255) ^ 5] * 100000 = 180604

Bank 3 (Monthly)

End of Year 1 = [(1+0.1268) ^ 1] * 100000 = 112680

End of Year 5 = [(1+0.1268) ^ 5] * 100000 = 181650

During initial Year Difference is not much but as the year passes compounding effect come into the picture. There is a one-word answer “Compounding Effect” which increases as now of period Increases.

D) On Financial Calculator type

N = 25

I/Y = 4.5

PMT = 1000 * 3.5% = 35

FV = 1000

Then press CPT and then PV

Answer = 851.72

A sovereign bond is a debt instrument which issued by the specific government. It can be denominated in both foreign and domestic currency. It promise to pay the buyer a certain amount of interest for a mentioned number of years and alos repay the face value on maturity.

E) On Financial Calculator type

N = 25

I/Y = 4.5

PMT = 0

FV = 1000

Then press CPT and then PV

Answer = 332.73

If there is no Coupon in between it is called Zero Coupon Bond. These types of bond are traded at deep discount. Which is Clearly visible from above calculations. It is beneficial Because company knows that they have to pay after a long period of time and they can invest in big project without worrying about interest Expenses.