# TVM Question 2

A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. Her plan is for the fund to be capable of awarding \$25,000 annually in perpetuity. The first scholarship is to be awarded and paid out exactly four years from today. The funds will be deposited into an account immediately and will grow at rate of 4%, compounded semiannually, for the foreseeable future. How much money must the inventor donate today to fund the scholarship?

A. \$528,150

B. \$549,487

C. \$574,253

The right answer is B, but I can’t understand why.

First we will calculate PV of perpetuity: \$25,000 / 4.04% (EAR of 4%) = \$618,811.88

Then: my calculation: N=8; I/Y=2; PMT=0; FV=618,811.88; CPT PV=-528,149.9822

Right calculation: N=3; I/Y=4,04; FV=-618,811.88; CPT PV=549,487

Question: Why they take only 3 years in calculating PV if they will start awarding ony after 4 years???

You calculated the value of an ordinary perpetuity; i.e., a perpetuity that is paid at the end of each period. Thus, your PV of the perpetuity is the value at time t = 3.

As always, drawing a timeline helps.

P/int is a perpetuity immediate whose focal date is 1 period before the first payment. Thus, your formula gives the value at time 3, not time 4 . A perpetuity due of (1+int) × P/int gives the value as of the time of the first payment .

A side check using the CF worksheet:

CF0=0, C01=0, F01=3, C02=25,000 F02=1,500 (or some other huuuge number) 2nd quit NPV I=4.04 CPT NPV 549,487.24

Ok, thank you. I got a point. I should’ve viewed it from the 3rd year prospective.