Annuity problem.

College Majors Business Majors
1

<p>I’ve been trying to solve this for hours but I cannot seem to get the answer</p>

<p>You are thinking of buying a craft emporium. It is expected to generate cash flows of $30,000 per year in years 1 through 5, and $40,000 per year in years 6 through 10. If the appropiate discount rate is 8%, what amount are you willing to pay for the emporium today?</p>

<p>A)135,288
B) 228,476
c) 167,943
D) 215,048</p>

<p>This is what i did:
Cash flow 1:</p>

<p>PV1 = 30,000 x (PVIFAr,t) whereas r = .08, t =5
PV1 = 30,000 x 3.9927
PV1 = 119,781</p>

<ul>
<li>Solving for PVIFAr,t I use this formula: 1 - [1/(1+r)^t] / r</li>
</ul>

<p>PV2 = 40,000 x (PVIFAr,t) whereas r = .08, t = 10
PV2 = 40,000 x 6.7101
PV2 = 268,404</p>

<p>Now I add PV1 and PV2 and together and get $388,185; the amount you should pay for the emporium. What am I doing wrong?</p>

2

<p>You need to break it up into two seperate annuities (PV1 and PV2) and then discount the second.</p>

<p>Present Value = Annunity Payment x [(1 - (1 + Discount Rate) ^ (- Periods)) / Discount Rate]</p>

<p>So PV1 = 30,000 x [(1 - (1 + .08) ^ (-5)) / .08]
PV1 = 30,000 x (3.99271)
PV1 = 119,781.3</p>

<p>Future Present Value 2 = 40,000 x 3.99271
Future Present Value 2 = 159,708.4
PV2 (Discounted back) = 159,708.4 / ((1.08) ^ 5)
PV2 = 108,694.9</p>

<p>PV1 + PV2 = 119,781.3 + 108,694.9</p>

<p>So the answer is 228,476.2 or B.</p>

3

<p>

</p>

<p>This assumes you are getting 40,000 for years 1 to 5 also. Which is wrong.<br>
You take present value of annuity to time = 6 then discount that amount as lump sum to time = 0 like what max did above.</p>

4

<p>The answer is B.</p>

<p>nPV(8,0,{30000,40000},{5,5}) = 22476.1556</p>

<p>You have 0 cash flows the first year…its just discounting back (1+.08) for every year back to time=0.</p>

5

<p>I meant it = 228476.1556</p>

6

<p>thanks for the correction. How do I enter this in a financial calculator? Like what are the steps? Doing this by hand takes so much time</p>

<p>5 = N
8 = I/Y
30,000 = PMT
0 = FV
CPT
PV = 119.781</p>

<p>5 = N
8 = I/Y
40,000 = PMT
0 = FV
CPT
PV = 159.708.4</p>

<p>What else do I have to enter?</p>

7

<p>This problem isn’t solved with the TVM because you have two different cash flows, therefore two different payments. If you have a TI 83/84, you open the Finance App and instead of hitting enter or 1 for the TVM Solver, you hit 7 and it says nPV( on the screen.</p>