Question

Question (1) (6 Marks) You are considering the purchase of a $ 1,500 face value of bond that pays 12% coupon interest per year and with maturity of 10 years, calculate the present value of the bond if: a) The Required rate of return (rrr) is 10%. (2 marks) b) The Required rate of return (rrr) is 13%. (2 marks) c) What do your answers to part (A) and (B) say about the relation between the present value and face value. (2 marks)

Answer 1

	Given,
	Face value of bond	$1,500
	Coupon rate	12% p.a.
	Maturity	10 years
	Annual cashflow	1500*12%
		$180
	Terminal cashflow	1500+(1500*12%)
		$1,680
a)	The present value of bond if the required rate of return is 10%
	Year	Cashflow	Discounting factor @ 10%	Present value of cashflows
	1	180	0.909090909	163.6363636
	2	180	0.826446281	148.7603306
	3	180	0.751314801	135.2366642
	4	180	0.683013455	122.942422
	5	180	0.620921323	111.7658382
	6	180	0.56447393	101.6053074
	7	180	0.513158118	92.36846128
	8	180	0.46650738	83.97132844
	9	180	0.424097618	76.33757131
	10	1680	0.385543289	647.7127262
		Present value of bond	1684.337013
b)	The present value of bond if the required rate of return is 13%
	Year	Cashflow	Discounting factor @ 13%	Present value of cashflows
	1	180	0.884955752	159.2920354
	2	180	0.783146683	140.966403
	3	180	0.693050162	124.7490292
	4	180	0.613318728	110.397371
	5	180	0.542759936	97.69678848
	6	180	0.480318527	86.45733494
	7	180	0.425060644	76.51091587
	8	180	0.376159862	67.70877511
	9	180	0.332884833	59.91927001
	10	1680	0.294588348	494.9084249
		Present value of bond	1418.606348
c)	We know that the present value is the value of future expected cashflows which would be received from the securities discounted at the required rate of return whereas face value is the value which the bond holder will realise on the date of maturity. In the above two solution, it can be concluded that the present value of bond decreases when the rate of return required from the investment increases given all the conditions i.e. face value, coupon rate and maturity constant. Further in the answer (a), the present value of the bond is greater than the face value of the bond this is because the required rate of return of 10% is less than the coupon rate of 12%. In answer (b), the present value of the bond is lesser than the face value of the bond this is because the required rate of return of 13% is more than the coupon rate of 12%.