Question

Using the Payback Method, IRR, and NPV Problems Purpose of Assignment The purpose of this assignment is to allow the student to calculate the project cash flow using net present value (NPV), internal rate of return (IRR), and the payback methods. Assignment Steps Resources: Corporate Finance Calculate the following time value of money problems in Microsoft Excel or Word document. You must show all of your calculations. If you want to accumulate $500,000 in 20 years, how much do you need to deposit today that pays an interest rate of 15%? What is the future value if you plan to invest $200,000 for 5 years and the interest rate is 5%? What is the interest rate for an initial investment of $100,000 to grow to $300,000 in 10 years? If your company purchases an annuity that will pay $50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase? What is the rate of return required to accumulate $400,000 if you invest $10,000 per year for 20 years. Assume all payments are made at the end of the period. Calculate the project cash flow generated for Project A and Project B using the NPV method. Which project would you select, and why? Which project would you select under the payback method? The discount rate is 10% for both projects. Use Microsoft® Excel® to prepare your answer. Note that a similar problem is in the textbook in Section 5.1. Sample Template for Project A and Project B: Show all work. Submit the all calcluations. Click the Assignment Files tab to submit your assignment.

Answer 1

1. FV = $500,000, n = 20, r = 15%

Let PV = x. Thus FV = PV*(1+r)^n

Or 500,000 = x*(1.15)^20

Or x = 500,000/1.15^20

= $30,550.14

2. This is the case of an annuity in which $200,000 is invested each year. n = 5 years and r = 5%. We can use the FVIFA (future value interest factor of annuity here). FVIFA (5 years, 5%) = 5.5256

Thus future value = 200,000*5.5256 = $1,105,120

(It has been assumed that amounts are deposited at the end of each year)

3. Let the interest rate be “r”

Thus 300,000 = 100,000*(1+r)^10

Or 3 = (1+r)^10

Or r = 11.61%

4. Here annuity starts at the beginning of the year.

Year	Amount	1+r	PVIFA	Present value
1	50,000.00	1.11	2.8394	50,000.00
2	50,000.00		2.5580	45,045.05
3	50,000.00		2.3045	40,581.12
4	50,000.00		2.0762	36,559.57
5	50,000.00		1.8704	32,936.55
6	50,000.00		1.6851	29,672.57
7	50,000.00		1.5181	26,732.04
8	50,000.00		1.3676	24,082.92
9	50,000.00		1.2321	21,696.32
10	50,000.00		1.1100	19,546.24
			Total	326,852.38

5. Here annuity = 10,000, n = 20 and FV = 400,000. As payments are made at the end of each year it is an ordinary annuity

Thus 400,000 = 10,000* FVIFA of an ordinary annuity for 20 years and r%

or 40 = FVIFA of an ordinary annuity for 20 years and r%

or 40 = 1/[(1+r)^20 - 1/r]

Thus r = 6.774%

6. This cannot be answered as the financial data and cash flow data for projects A and B is not provided.