Question

Advanced Time Value of Money Problems

Your child was just born and you are planning for his/her college education. Based on your wonderful experience in Financial Economics you decide to send your child to Hofstra University as well. You anticipate the annual tuition to be $60,000 per year for the four years of college. You plan on making equal deposits on your child’s birthday every year starting today, the day of your child’s birth. No deposits will be made after starting college. The first tuition payment is due in exactly 18 years from today (the day your child turns 18 – no deposit required, i.e. last deposit is on 17th birthday). Assume the annual expected return on your investments is 10% over this period.

1. (i) Calculate the annual deposit.

2. (ii) Calculate the amount needed if only equal annual deposits are made on birthday’s 5-10 inclusive.

3. (iii) Calculate the amount needed if two equal annual deposits are made on birthday’s 5 and 13.

4. (iv) Answer part (i), now assume tuition rises 10% per year.

5. (v) Answer part (i) assuming first deposit will be made on your child’s 1st birthday. All other information is the same. What is the annual tuition payment? How does it compare to part (i)? Is your answer surprising?

Answer 1

Tution Fees per years is $60,000 for 4 years

Assuming that tution fees is to be made at the beginning of every year

Expected Return on investment is 10%

(i)

Present value of Investment required at the end of 17th year =60,000+ 60,000*PVIFA(10%, 3 years) = $209211

Annual amount to deposited from 0 to 17 years is as follows

=

209211

1+ (1+0.1)raise to 17

=

209211

45.6

=

$4,587.96

(ii)

If only equal deposits are to be made between 5th to 10 years

Present value of investment at the end of of 11th year is as follows

=

209211

PVIFA(10%, 6)

=

$118094

Equal annual deposits needed are as follows

118094

(1+0.1) raises to 5

$13914

(iii)

Annual amount to be deposited on 5th and 13th birthday

If $ 1 is invested on 5th birthday then if would hve become $ 3.138 at the end of 17th year

Similarly, If $ 1 is invested on 5th birthday then if would hve become $ 1.464 at the end of 17th year

Hence if goes in same line then, $ 209211 has to be bifurcated, then

Amount invetsed in 5th year is ((209211*3.138)/(3.138+1.464))*PVIF(10%, 12) = 142656*0.3186=45455

Amount invetsed in 5th year is ((209211*1.464)/(3.138+1.464))*PVIF(10%, 4) = 66554.73*0.683=45457

(iv)

Year end

Tution fees

17

60000

18

66000

19

72600

20

79860

Present value of Investment required at the end of 17th year = 240000

Annual amount to deposited from 0 to 17 years is as follows

=

240000

1+ (1+0.1)raise to 17

=

240000

45.6

=

$5263