Question

An heiress has a rich grandfather who set up a trust that will pay her $5 million per year for 20 years beginning on her 25th birthday. Assume her 25th birthday is 4 years from now. Further assume that you are a wealthy investor and this heiress is anxious to get her hands on some serious cash. You are offered the opportunity to purchase the rights to receive the promised cash flows from the trust.

a.  If you were to pay $80 million today for the right to receive these cash flows promised to the heiress, what is the net present value (NPV) of this investment, assuming a 10% discount rate is appropriate?

b.  What is the internal rate of return (IRR) of this $80 million investment?

Answer 1

(a)	We will receive 5 million for 20 years beginning from t=4
	Annual cash inflow =				5	(Million)
	Annuity factor(10%,4-24)			= Annuity factor for 24 years - annuity factor for 3 years
	PVAF(10%,24)				8.9847
Less:	PVAF(10%,3)				2.4869
	Annuity factor(10%,4-24)				6.4979
	PV of annual cash inflows =			5 x 6.499 =	32.48946
Less:	Initial investment =				80.00000
	NPV =				-47.51054
(b)	IRR is the rate at which the NPV becomes 0.
	PVAF(r,4-24) x 5 = 80
	PVAF(r,4-24) =		80/5
	PVAF(r,4-24) =		16
	Using linear interpolation -
	Rate	PVAF(r,24)	PVAF(r,3)	PVAF(r,4-24)
	3%	16.94	2.83	14.11
	r			16.00
	2%	18.91	2.88	16.03
	Using interpolation -
	r-2/3-2 =	16-16.03/14.11-16.03
	r-2 =	-0.03/-1.92
	r-2 =	0.015622
	r =	2.015622
		APPROX
	In case you can use excel
	Alternative solution
A	B	C	D	E
35	Years	Cash flow
36	0	-80
37	1	0
38	2	0
39	3	0
40	4	5
41	5	5
42	6	5
43	7	5
44	8	5
45	9	5
46	10	5
47	11	5
48	12	5
49	13	5
50	14	5
51	15	5
52	16	5
53	17	5
54	18	5
55	19	5
56	20	5
57	21	5
58	22	5
59	23	5
60	24	5
61
62		NPV=	-47.5105	=NPV(10%,C37:C60)+C36
63		IRR =	2.0144%	=IRR(C36:C60)
64
65