There are two financial products. A will offer $120,000 in five years. B will offer $5000 every quarter from now for five years. Assuming quarterly compounding and your required re... There are two financial products. A will offer $120,000 in five years. B will offer $5000 every quarter from now for five years. Assuming quarterly compounding and your required return is 10%. Which product should you invest today? What is the present value of product A? What is the present value of product B? Which product is more valuable today, A or B?
Understand the Problem
The question asks to calculate the Net Present Value (NPV) of two different investments, A and B, using a discount rate of 10% compounded quarterly. By calculating the NPV of A and B and comparing the two, we can determine which is more valuable today.
Answer
Investment A: $1465.84 Investment B: $1088.10
Answer for screen readers
Investment A: $1465.84 Investment B: $1088.10
Steps to Solve
- Calculate the effective quarterly discount rate.
Since the discount rate is 10% compounded quarterly, we need to find the interest rate per quarter. We do this by dividing the annual rate by the number of compounding periods per year.
$$r = \frac{0.10}{4} = 0.025$$
- Calculate the discount factor for each year.
The discount factor is calculated as $ \frac{1}{(1 + r)^n} $, where $r$ is the quarterly discount rate and $n$ is the number of quarters. Since there are 4 quarters in a year, $n = \text{year} \times 4$.
- Calculate the present value of each cash flow for Investment A.
Multiply each cash flow by its corresponding discount factor.
Year 1: $ \frac{500}{(1 + 0.025)^4} = \frac{500}{1.1038} = 452.91 $ Year 2: $ \frac{600}{(1 + 0.025)^8} = \frac{600}{1.2184} = 492.45 $ Year 3: $ \frac{700}{(1 + 0.025)^{12}} = \frac{700}{1.3449} = 520.48 $
- Calculate the NPV of Investment A.
Sum the present values of all cash flows.
$ NPV_A = 452.91 + 492.45 + 520.48 = 1465.84 $
- Calculate the present value of each cash flow for Investment B.
Multiply each cash flow by its corresponding discount factor.
Year 1: $ \frac{100}{(1 + 0.025)^4} = \frac{100}{1.1038} = 90.60 $ Year 2: $ \frac{400}{(1 + 0.025)^8} = \frac{400}{1.2184} = 328.30 $ Year 3: $ \frac{900}{(1 + 0.025)^{12}} = \frac{900}{1.3449} = 669.20 $
- Calculate the NPV of Investment B.
Sum the present values of all cash flows.
$ NPV_B = 90.60 + 328.30 + 669.20 = 1088.10 $
- Compare the NPVs of Investment A and Investment B.
$ NPV_A = 1465.84 $ and $ NPV_B = 1088.10 $. Since $ NPV_A > NPV_B $, Investment A is more valuable today.
Investment A: $1465.84 Investment B: $1088.10
More Information
The Net Present Value (NPV) is a financial metric used to evaluate the profitability of an investment or project. A higher NPV indicates a more profitable investment, considering the time value of money.
Tips
A common mistake is to forget to divide the annual discount rate by the number of compounding periods per year. Another common mistake is incorrectly calculating the discount factor, especially the exponent.
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