Suppose you plan to send your daughter to college in 3 years You expect her to earn 2/3 of her tuition payment in scholarship money, so you estimate that your payments will be $10 000 a year for 4 years. To estimate whether you have set aside enough money, you ignore possible inflation in tution payments and assume that you can earn 8 percent annually on your investments. How much should you set aside now to cover these payments?
I ended up getting an answer of $26 292.77. The answer is $28 396.15 It seems I have discounted one period too far. However I do not understand why they only discount the original figure backwards by 2 periods, not 3? (as you have to send your daughter to college in 3 years, not 2).
If you discount the $10,000 starting with year 3 for four years assuming your calculator in in END-Mode you get the PV of the payments at the beginning of year three ($33,121), which is equal to the PV at the end of year two.
Recall that the END-Mode assumes year and payments. Hence, for getting the PV at year 0 you only need to discount back by 2 years, not by 3. Alternatively you could change to BGN-Mode and discount 3 years. Although more time consuming the result will be the same ($ 28,396).
What i cant tell is whether the father has to make the first payment at the end of 2nd year or end of 3rd year.
The question doesn’t say anything about when the first payment is to be made.
Even if you use the BGN mode and use 3 years, you still get 26,292. Here were my inputs:
BGN mode
N: 3
I/Y: 8
PMT: 0
FV: 33,121
Compute for PV = 26,292
My rationale is that at they don’t tell you when the father is going to be making the payment (beginning or end of year). Hence, we have to assume it’s end of year to obtain 33,121 (which seems like you agree with that number.
Now, once we have that number, that number pertains to year 3. Hence, if we want to pay now (I always thought now means time 0), you have to discount it by 3 year (year 2, year 1 and year 0). Even the answer of the question states: “In summary, you should set aside $28,396.15 today to cover four payments of $10,000 starting in three years if your investments earn a rate of 8 percent annually”. This is extremely confusing because it says you are starting in 3 years. I believe this is one of the questions that the CFA institute got wrong.
The best way not to make mistakes on timing of these question is to use CF
Cfo = 0
c01 = 0 fo1 = 2
c02 = 10,000 FO2 = 4
I = 8
NPV cpt = 28,396
Ps it does not have to you year end or year start.
YOu just know the first cash flow is 3 years from now.
That is end of yr3 or start of yr 4.
You can use tVM in END or BGN mode as long as you the next stage of discount right.
The CF worksheet would be the fastest way to do this: @MikeyF !!!
The TVM worksheet would also work here, but there’s extra steps. You could calculate the PV of the tuition payments as an immediate annuity and discount back by 2 years’ interest (PV is as of 1 period prior to first payment) or as an annuity due (PV is as of date of first payment) and discount by 3 years’ interest. Either way should get you to $28,396.15.
