BBA307: Finance


Exercise 8A


Assignment 8.1








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?

Submission


--------------------------------------------------------------------------------

To answer the questions step-by-step:

1. To calculate the NPV for each franchise, we need to discount the cash flows to their present value and subtract the initial investment. The formula to calculate NPV is:

NPV = CF0 + (CF1/(1+r) + CF2/(1+r)^2 + CF3/(1+r)^3)

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

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

2. If franchises are independent, we would accept both franchises if their NPV is positive. If franchises are mutually exclusive, we would accept the franchise with the highest NPV.

3. The NPV would change if the cost of capital changed because the discount rate (r) affects the present value of the cash flows.

4. To calculate the IRR for each franchise, we need to find the discount rate that makes the NPV equal to zero. We can use trial and error or financial calculators to find the IRR.

5. The IRR method uses the discount rate that makes the NPV equal to zero. If the IRR is greater than the required rate of return, the project is acceptable. If franchises are independent, we would accept the franchise with the highest IRR. If franchises are mutually exclusive, we would accept the franchise with the IRR greater than the required rate of return.

6. The franchises' IRR would change if the cost of capital changed because the discount rate affects the calculation of IRR.

7. NPV profiles show the relationship between the discount rate and NPV. To draw the NPV profiles, we plot the NPV values at different discount rates. The profiles will cross at a discount rate where the NPV for one franchise becomes higher than the other.

8. Using the NPV profiles, if franchises are independent, we would accept both franchises when the discount rate is below the point where the profiles cross. If franchises are mutually exclusive, we would accept the franchise with the higher NPV when the discount rate is below the point where the profiles cross. At any cost of capital less than 23.6%, the answers would be correct.

9. The best method depends on the specific circumstances and preferences of the investor. NPV method is considered more reliable since it considers the time value of money and provides a more accurate measure of profitability. However, IRR method is useful for comparing projects and making decisions based on the return on investment.

To determine the answers to the questions in Assignment 8.1, we need to calculate the NPV and IRR for both franchises L and S, and analyze their profiles.

1. To calculate the NPV for each franchise, we need to discount the cash flows for each year using the required rate of return of 10%. The NPV formula is as follows:

NPV = CF0 + (CF1 / (1+r)^1) + (CF2 / (1+r)^2) + (CF3 / (1+r)^3)

- For Franchise L:
NPV = $100 + ($10 / (1+0.10)^1) + ($60 / (1+0.10)^2) + ($80 / (1+0.10)^3)

- For Franchise S:
NPV = $100 + ($70 / (1+0.10)^1) + ($50 / (1+0.10)^2) + ($20 / (1+0.10)^3)

2. According to the NPV, if the franchises are independent, we should accept the franchise with the highest positive NPV. If they are mutually exclusive, we should accept the franchise with the higher NPV without considering the other.

3. Yes, the NPV would change if the cost of capital changed. As the required rate of return increases or decreases, the present value of future cash flows changes, affecting the NPV.

4. To calculate the IRR for each franchise, we need to find the discount rate that makes the NPV equal to zero. We can use the IRR formula to find this rate.

IRR = Discount rate where NPV = 0

5. The IRR method is based on finding the discount rate that makes the present value of future cash flows equal to the initial investment. According to the IRR, if the franchises are independent, we should accept the franchise with the highest IRR. If they are mutually exclusive, we should accept the franchise with the higher IRR without considering the other.

6. Yes, the franchises' IRR would change if the cost of capital changed. The IRR is directly affected by the discount rate, so any change in the required rate of return would result in a different IRR.

7. To draw the NPV profiles for each franchise, we need to calculate the NPVs for different discount rates. We can plot the discount rate on the X-axis and the NPV on the Y-axis. The point where the profiles cross represents the discount rate where the NPVs of both franchises are equal.

8. By examining the NPV profiles, we can determine the discount rate at which the profiles cross. Below that rate, the franchise with the higher NPV should be accepted, both if they are independent or mutually exclusive. Above that rate, neither franchise should be accepted.

9. The best method depends on the specific circumstances and requirements of the investor. Both NPV and IRR provide useful information, but NPV is generally considered more reliable as it takes into account the time value of money and explicitly considers the discount rate. IRR, on the other hand, can have multiple solutions and may not always provide a clear decision criterion.

To submit your assignment, you should provide your calculations for NPV, IRR, and a detailed explanation of your answers to each question.