Question

YOU HAVE TO DO QUESTION 7 ONLY, QUESTION 4 AND 5 and 6 ARE FOR REFERENCE

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?

Q7. Calculate the current yield, the capital gains yield, and the duration of the bond (price is found in Q5 which was 968) and state How would the composition of capital gain yield and current yield for this bond changes over time, as the bond approaches to the maturity.?

Answer 1

Q5) FV face value = 1000

c coupon rate = 8% = 8% * 1000 = 80

MV market value of bond = 968

t time to maturity = 5 years

y yield to maturity = ?

To calculate y, we will substitute the value of y in RHS of equation

Since MV is less than FV (y should be higher than c) ie y > 8%

Hit & trail

y = 9%, value = 961.1013

y = 9.5%, value = 942.4044

y = 8.5%; value = 980.2968

It is clear y lies between 9% & 8.5%

Using linear interpolation

y = 9% - {( 968 - 961.1013)/(980.2968 - 961.1013)}*0.5% = 9% - 0.18% = 8.82%

Issue price of bond = 1000 (as per Q5, coupon = yield = 8%. Therefore MV of bond = FV of bond)

Capital gain yield = (968 - 1000)/1000 = -0.032 = -3.2%

Duration of bond

	Bond
Settlement date	1-Apr-20
Maturity date	1-Apr-25
Coupon	8.0%
Yield	8.82%
Duration	4.299607
	=DURATION(B2,B3,B4,B5,1)

Duration of bond = 4.29 years

As bond reaches maturity, the yield of bond will become closer to coupon rate ie 8% & the capital yield will become closer to original yield to maturity ie 8%