Question

A wealthy philanthropist has established the following endowment for a hospital. The details are as follows: a cash deposit of $ 15 M one year from now; an annual cash deposit of $3M per year for the next five years. The first $3M will start today. At the end of 5 years, the hospital will also receive a lump sum payment of $19M. Assuming the cost of money is 4%, what is the value of this endowment in today’s dollars?

Answer 1

1	B	C	D	E	F	G
2	Time Period	Cash InFlow or Income in USD and Million	Factors using Return Rate 4%	Present Value of Cash InFlow or Income at Return Rate of 4%	Cash Outflow or Cost in USD and Million	Present Value of Cash Outflow or Cost at Return Rate of 4%
3	0		1	0	3	3
4	1		0.961538462	0	15	14.42307692
5	1		0.961538462		3	2.884615385
6	2		0.924556213	0	3	2.773668639
7	3		0.888996359	0	3	2.666989076
8	4		0.854804191	0	3	2.564412573
9	5	19	0.821927107	15.61661503
10	Total Present Value	NA	NA	15.61661503	NA	28.3127626
11	Net Present Value or NPV	-12.70

The value of this endowment in today’s dollars = USD 12.70 Million (Negative)

Formula

1	B	C	D	E	F	G
2	Time Period	Cash InFlow or Income in USD and Million	Factors using Return Rate 4%	Present Value of Cash InFlow or Income at Return Rate of 4%	Cash Outflow or Cost in USD and Million	Present Value of Cash Outflow or Cost at Return Rate of 4%
3	0		=1/(1+0.04)^B3	=C3*D3	3	=F3*D3
4	1		=1/(1+0.04)^B4	=C4*D4	15	=F4*D4
5	1		=1/(1+0.04)^B5		3	=F5*D5
6	2		=1/(1+0.04)^B6	=C6*D6	3	=F6*D6
7	3		=1/(1+0.04)^B7	=C7*D7	3	=F7*D7
8	4		=1/(1+0.04)^B8	=C8*D8	3	=F8*D8
9	5	19	=1/(1+0.04)^B9	=C9*D9
10	Total Present Value	NA	NA	=SUM(E3:E9)	NA	=SUM(G3:G8)
11	Net Present Value or NPV	=E10-G10