Question

At a constant interest rate of 15%, compounded annually, what is the present value of an income stream paying $50 next quarter and growing at 2% per quarter until the end of the third year? From that point on it grows at 1% per quarter indefinitely.

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		Annual Interest rate=15%
		Quarterly interest rate=i
		(1+i)^4=1.15
		1+i=1.15^(1/4)=	1.035558
		i=0.035558
		N=Quarter of Cash Flow
		N	A	B=A/(1.03558^N)
		Quarter	Cash Flow	Present Value
	A	1	$50	$48.28
	B=A*1.02	2	$51.00	$47.56
	C=B*1.02	3	$52.02	$46.84
	D=C*1.02	4	$53.06	$46.14
	E=D*1.02	5	$54.12	$45.45
	F=E*1.02	6	$55.20	$44.76
	G=F*1.02	7	$56.31	$44.09
	H=G*1.02	8	$57.43	$43.43
	I=H*1.02	9	$58.58	$42.78
	J=I*1.02	10	$59.75	$42.13
	K=J*1.02	11	$60.95	$41.50
	L=K*1.02	12	$62.17	$40.88	$533.84	SUM
	M=L*1.01	13	$62.79	(62.17*1.01)
		Value of income stream from quarter 13 to perpetuity at end of year 3	$2,456.78	(62.79/(0.035558-0.01)
		Value of income stream from quarter 13 to perpetuity at PRESENT	$1,615.37	2456.78/(1.15^3)
		PRESENT VALUE OF TOTAL INCOME STREAM	$2,149.21	(533.84+1615.37)