Suppose you invest $3500 today and receive $9500 in five years. a. What is the IRR of this opportunity? b. Suppose another investment opportunity also requires $3500 upfront, but pays anequal amount at the end of each year for the next five years. If this investment has thesame lRk ds the first one, what is the amount you will receive cach year?
Question
Suppose you invest 9500 in five years. a. What is the IRR of this opportunity? b. Suppose another investment opportunity also requires $3500 upfront, but pays anequal amount at the end of each year for the next five years. If this investment has thesame lRk ds the first one, what is the amount you will receive cach year?
Solution
a. The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows (both positive and negative) from a particular project equal to zero. It can be calculated using the formula:
0 = -3500 + 9500 / (1 + IRR)^5
Solving this equation for IRR is a bit complex as it involves solving for a variable in the exponent, which usually requires numerical methods. However, using a financial calculator or software like Excel, you can find that the IRR for this investment is approximately 22.02%.
b. If another investment opportunity has the same IRR, it means that the present value of its cash flows, discounted at this rate, must also equal the initial investment of $3500.
Let's denote the unknown equal annual payment as X. The equation becomes:
3500 = X/(1+0.2202) + X/(1+0.2202)^2 + X/(1+0.2202)^3 + X/(1+0.2202)^4 + X/(1+0.2202)^5
Again, solving this equation for X requires a financial calculator or software like Excel, and you will find that X is approximately 1000 at the end of each year for the next five years.
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