Question

YOU HAVE TO DO QUESTION 6 ONLY, QUESTION 4 AND 5 ARE FOR REFERENCE, ANSWER FOR 5 IS ALREADY PROVIDED.

Q4. What is the value of a 5-year, AED 1,000 par value bond with an 8% annual coupon if the YTM (required rate of return) of return is 8%? Explain to the manager of the firm without calculation.

Q5. (i). What would be the value of the bond if, just after it had been issued, the expected inflation rate rose by 2%, causing investors to require a 10% return? Would we now have a discount or a premium bond? (ii). What would happen to the value of this bond over time if the required rate of return remained at 10% until maturity? Show with a graph and explain to the manager.

Q6. (i). What is an approximation of the yield to maturity for this bond if the bond is selling at AED 900? (ii). Explain the management what your fears are, and you believe that the selling price would reach AED 900?

Answer 1

Q6) FV (par value) = 1000

C coupon (paid annually) = 8% = 8%*1000 = 80

MV market value = 900

y yield to maturity = ?

t time to maturity = 5 year

To calculate the value of y we will have to use hit & trail method. Since the MV of bond is less than FV (ie 900 < 1000) the yield to maturity will be greater than coupon rate (ie y > 8%)

Substitute the value of y in RHS of the above equation and find the value:

Substitute y in:

y = 9%; value = 961.1036

y = 10%; value = 924.1843

y = 11%; value = 889.1231

It is clear that the value of y lies between 10% & 11%

Using linear extrapolation

y = 11% - {(900 - 889.1231)/(924.1843 - 889.1231)}*1% = 11% - 0.31% = 10.69%

(ii) When you bought the bond yield to maturity (ytm) was 8% (as per Q4). Now the yield has increased to 10.69%. As ytm increases, the value of bond depreciates. So your fears are ytm increases beyond & 10.69% and bond depreciates in market value.