Question

9 your friend brought up an investment opportunity that will generate cash flows of $5,000, $5,300, and $6,000 next three years, respectively. if your required rate of return on this investment is 12%, how much at most are you willing to pay? round to the nearest cent. do not include any unit (if your answer is $111.11, then type 111.11 without $ sign.)

Explanation:

Step1: Define present value formula

The present value (PV) of a future cash flow $CF_n$ at time $n$ with discount rate $r$ is $\text{PV} = \frac{CF_n}{(1+r)^n}$. We sum PVs of all cash flows.

Step2: Calculate PV of Year 1 cash flow

$CF_1 = 5000$, $r=0.12$, $n=1$
$\text{PV}_1 = \frac{5000}{(1+0.12)^1} = \frac{5000}{1.12} \approx 4464.2857$

Step3: Calculate PV of Year 2 cash flow

$CF_2 = 5300$, $n=2$
$\text{PV}_2 = \frac{5300}{(1+0.12)^2} = \frac{5300}{1.2544} \approx 4225.29$

Step4: Calculate PV of Year 3 cash flow

$CF_3 = 6000$, $n=3$
$\text{PV}_3 = \frac{6000}{(1+0.12)^3} = \frac{6000}{1.404928} \approx 4270.68$

Step5: Sum all present values

$\text{Total PV} = 4464.2857 + 4225.29 + 4270.68$

Answer:

12960.26