Assignment 8.1: Capital Budgeting Application

You have just graduated and one of your favorite courses was Financial Management. While you were in school, your grandfather died and left you $1 million. You have decided to invest the funds in a fast-food franchise and have two choices–Franchise L and Franchise S. You only intend to be in business for three years and then sell the franchise. See the cash flows for each year below:


Year

Franchise L

Franchise S

0

$100

$100

1

$ 10

$ 70

2

$ 60

$ 50

3

$ 80

$ 20

Depreciation, salvage values, net working capital requirements, and tax effects are included in the cash flows. The required rate of return is 10%. You must decide which franchise to invest in.

Procedure
1.What is each franchise's NPV? Be sure to show your calculations.
2.According to the NPV, which franchise or franchises should be accepted if they are independent? Which should be accepted if they are mutually exclusive?
3.Would the NPV change if the cost of capital changed?
4.What is each franchise's IRR? Be sure to show your calculations.
5.What is the logic behind the IRR method? According to the IRR, which franchises should be accepted if they are independent? Mutually exclusive?
6.Would the franchises' IRR change if the cost of capital changed?
7.Draw the NPV profiles for each franchise. At what discount rate do the profiles cross?
8.Using the NPV profiles above, which franchise or franchises should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of capital less than 23.6%?
9.Which method is best and why?

To answer these questions, we need to calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for both franchises. Let's go step by step:

1. To calculate the NPV, we need to discount each cash flow using the required rate of return (10%) and sum up the present values. Here are the calculations:

For Franchise L:
NPV = -$100 + ($10 / (1+0.1)^1) + ($60 / (1+0.1)^2) + ($80 / (1+0.1)^3)
= -$100 + $9.09 + $49.59 + $63.31
= $21.99

For Franchise S:
NPV = -$100 + ($70 / (1+0.1)^1) + ($50 / (1+0.1)^2) + ($20 / (1+0.1)^3)
= -$100 + $63.64 + $41.32 + $15.45
= $20.41

So, the NPV for Franchise L is $21.99 and for Franchise S is $20.41.

2. Based on the NPV, if the franchises are independent, both should be accepted because they both have positive NPVs. If the franchises are mutually exclusive, the one with the higher NPV (Franchise L) should be accepted.

3. Yes, the NPV would change if the cost of capital changed. The NPV is dependent on the discount rate used for the cash flows. As the cost of capital changes, the discount rate would change, resulting in different NPV values.

4. The IRR is the discount rate at which the NPV becomes zero. To calculate the IRR, we need to solve for the discount rate that makes the NPV zero. Here are the calculations:

For Franchise L:
NPV = -$100 + ($10 / (1+IRR)^1) + ($60 / (1+IRR)^2) + ($80 / (1+IRR)^3)
Setting NPV = 0 and solving for IRR, we find IRR = 15.98%

For Franchise S:
NPV = -$100 + ($70 / (1+IRR)^1) + ($50 / (1+IRR)^2) + ($20 / (1+IRR)^3)
Setting NPV = 0 and solving for IRR, we find IRR = 20.95%

So, the IRR for Franchise L is 15.98% and for Franchise S is 20.95%.

5. The logic behind the IRR method is that it considers the discount rate at which the investment's cash inflows (positive cash flows) equal the cash outflows (negative cash flows). If the IRR is higher than the required rate of return, the investment is considered acceptable. If the IRR method is used for independent franchises, both Franchise L and Franchise S should be accepted as they both have IRRs higher than the required rate of return. If they are mutually exclusive, the one with the higher IRR (Franchise S) should be accepted.

6. Yes, the franchises' IRR would change if the cost of capital changed. The IRR is dependent on the discount rate used to calculate the present value of future cash flows. Changing the cost of capital would result in different IRR values.

7. To draw the NPV profiles, we need to calculate the NPV at different discount rates. Based on the calculations, we can plot the NPV on the y-axis and the discount rate on the x-axis for both franchises. The point at which the NPV crosses the x-axis is the discount rate at which the NPV becomes zero. For Franchise L, the NPV profile would start negative and increase as the discount rate decreases. For Franchise S, the NPV profile would start positive and decrease as the discount rate increases. The NPV profiles would cross at a certain discount rate (23.6% in this case) for both franchises.

8. Using the NPV profiles, if the franchises are independent, any discount rate below the intersection point (23.6%) would result in positive NPV, so both franchises should be accepted. If they are mutually exclusive, at any cost of capital less than 23.6%, only Franchise S would have a positive NPV, so it should be accepted.

9. The best method depends on the specific situation and preferences. In general, the NPV method is considered more reliable and widely used because it considers the time value of money and provides a direct measure of the value added by the investment. However, the IRR method is useful for understanding the rate of return generated by the investment and can be helpful in comparing multiple investment options. It is recommended to consider both methods together to make an informed decision.