Question

company has an investment project that would cost $10 million today and yield a payoff of $15 million in 4 years. (Make sure to show all your work.)a.Calculate the present value if the interest rate is 11 percent.Should the firm undertake the project if the interest rate is 11 percent? Why?b.Calculate the present value if the interest rate is 10 percent.Should the firm undertake the project if the interest rate is 10 percent? Why?c.Calculate the present value if the interest rate is 9 percent.Should the firm undertake the project if the interest rate is 9 percent? Why?

Answer 1

The present value of the investment project at 11%, 10%, and 9% interest rates are $10.24 million, $10.45 million, and $10.63 million, respectively. At all these interest rates, the present value exceeds the initial investment cost of $10 million, suggesting the project is financially viable at each rate.

Step-by-step explanation:

To calculate the present value (PV) of the investment project, we use the formula PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of time periods. Here, FV is $15 million, and n is 4 years.

(a) At 11% interest rate:

PV = $15 million / (1 + 0.11)^4 = $15 million / 1.4641 = $10.24 million.

Since the PV at 11% ($10.24 million) is greater than the investment cost ($10 million), the firm should undertake the project.

(b) At 10% interest rate:

PV = $15 million / (1 + 0.10)^4 = $15 million / 1.4641 = $10.45 million.

Since the PV at 10% ($10.45 million) is greater than the investment cost, the project is more favourable.

(c) At 9% interest rate:

PV = $15 million / (1 + 0.09)^4 = $15 million / 1.4116 = $10.63 million.

With a PV of $10.63 million at a 9% interest rate, the project is still feasible as it exceeds the cost of the investment.

Answer 2

a. I = 11%

NPV = -$119,035.39

The firm shouldn't undertake the project because the present value is negative.

b. I = 10%

NPV = $245,201.83

The firm should undertake the project because the present value Is positive.

c. I = 9%

NPV = $626,378.17

The firm should undertake the project because the present value Is positive.

Step-by-step explanation:

Net present value is the present value of after tax cash flows from an investment less the amount invested.

The decision rule is to not to undertake a project if its present value is negative and undertake it if it is positive.

The present value can be calculated using a financial calculator.

Cash flow in year zero = -$10 million

Cash flow each year from year 1 to 3 = 0

Cash flow in year 4 = $15 million

a. I = 11%

NPV = -$119,035.39

b. I = 10%

NPV = $245,201.83

c. I = 9%

NPV = $626,378.17

To find the NPV using a financial calacutor:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.

3. Press compute

I hope my answer helps you