TVM Question

CFA Level I Quant
#1

Hi all,

I struggle with TVM questions, mostly the annuity due problems. I’ve tried drawing timelines, and it doesn’t seem to help. Will somebody please explain how this should be entered into the calculator?

From the Schweser book:

A client plans to retire in 15 years and will need to withdraw $50,000 from his retirement account each year for 10 years, beginning on the day he retires. After that, he will need to withdraw $20,000 per year for 25 years. The account returns 4% annually. The amount he needs to have in the account on the day he retires is closest to:

A. $580,000

B. $640,000

C. $655,000

The answer is B, as the amount comes out to $641,284.

Also, if anyone can help me to understand how to work through these problems, I’d greatly appreciate it.

Thanks.

#2

You can use the TVM worksheet or the CF worksheet (CF is much fewer keystrokes!!).

TVM needs to be done in 2 pieces:

2nd pmt, 2nd set to BGN, 2nd quit

2nd set i/y make sure P/Y=C/Y=1

2nd clr tvm

35 N 4 I 20000 PMT CPT PV -388,223.95

10 N 30000 PMT CPT PV -253,059.99

388,223.95 + 253,059.99 =641,283.90

CF worksheet

2nd ce/c

CF0 50000 C01=50,000 F01=9 C02=20,000 f02=25 2nd quit npv 4 i cpt npv 641,283.90

#3

By the way, drawing a timeline can help immensely.

#4

Thanks breadmaker. I was trying to do it by finding the PV of $50,000 for 10 years and $20,000 for 25 years. I just realized the mistake I was making was not discounting the PV of the $20,000 payments at year 10 an additional 10 years.

To your point S2000, I now understand how a timeline would’ve helped there. The beginning/end of periods is what confuses me with timelines. For example, if a payment occurs at the beginning of year 5 and I wanted to find the PV of that payment, would I put that at year 5 on the timeline or year 4? I’m thinking at year 4 since it would be discounted 4 periods instead of 5. Maybe I’m overcomplicating this.

#5

If you actually draw the timeline, you should see your answer pretty easily.

Year 1 runs from time t = 0 to time t = 1.

Year 2 runs from time t = 1 to time t = 2.

.

.

.

Year 5 runs from time t = 4 to time t = 5.

So a payment at the beginning of year 5 occurs at time t = 4.

#6

Thanks S2000. It makes sense now. I’ll be drawing timelines going forward.

#7

My pleasure.

#8
  • the calculator manual has this very problem solved with key by key instructions.
#9

Curiosity question: how does the manual suggest solving the problem?

#10

You need to press g 7 (i.e. beg - to signify that the first cashflow happens at the beginning) to tell the calculator that you’re working with an annuity due.