Financial Management Midterm Exam (Part 2)

Explanation
Using the even cash flow distribution assumption, the project will completely recover the initial investment after P30/P35 = 0.86 of Year 5:
Payback = 4 + = 4.86 years.

Explanation
The PV of the outflows is -700 million. To find the discounted payback you need to keep adding cash flows until the cumulative PVs of the cash inflows equal the PV of the outflow:

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -700 million -700.0000 -700.0000
1 200 million 181.8182 -518.1818
2 370 million 305.7851 -212.3967
3 225 million 169.0458 -43.3509
4 700 million 478.1094 434.7585

The payback occurs somewhere in Year 4. To find out exactly where, we calculate 43.3509/478.1094 = 0.0907 through the year. Therefore, the discounted payback is 3.091 years.

Explanation
Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -3,000 -3,000.00 -3,000.00
1 1,000 909.09 -2,090.91
2 1,000 826.45 -1,264.46
3 1,000 751.31 -513.15
4 1,000 683.01 169.86

After Year 3, you can see that you won’t need all of Year 4 cash flows to break even. To find the portion that you need, calculate 513.15/683.01 = 0.75. Therefore, the discounted payback is 3.75 years.

Explanation
Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -300 -300.00 -300.00
1 100 100/(1.10) = 90.91 -209.09
2 150 150/(1.10)2 = 123.97 -85.12
3 200 200/(1.10)3 = 150.26 65.14
4 50 50/(1.10)4 = 34.15

From the cumulative cash flows we can see that the discounted payback is somewhere between 2 and 3 years. We assume that the 150.26 is received evenly throughout the third year. So, the initial outlay is recovered in 2 + 85.12/150.26, or 2.57 years.

Explanation
At a cost of capital of 15%, both projects have negative NPVs and, thus, both would be rejected.

Explanation
Financial calculator solution:
Inputs: CF0 = 0; CF1 = -100; Nj = 19; CF2 = 3210. Output: IRR = 5.0%.

Explanation
The regular payback period is the time it takes for the project's cash flows to equal the initial investment. In this case, the regular payback period is 2.25 years. The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project's cash flows equal to zero. To find the IRR, we need to calculate the NPV of the cash flows at different discount rates until we find the rate that gives an NPV of zero. The IRR for this project is 33.5%, which means that at a discount rate of 33.5%, the present value of the cash flows equals the initial investment.

Explanation
The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment. To calculate the discounted payback, we need to calculate the present value of each cash flow using the cost of capital of 10%. The present value of each cash flow is calculated as follows: Year 1: $50,000 / (1 + 0.10)^1 = $45,454.55 Year 2: $100,000 / (1 + 0.10)^2 = $82,644.63 Year 3: $150,000 / (1 + 0.10)^3 = $112,233.45 Year 4: $40,000 / (1 + 0.10)^4 = $28,925.62 Year 5: $25,000 / (1 + 0.10)^5 = $15,248.42 Now we can calculate the cumulative discounted cash flows: Year 1: $45,454.55 Year 2: $45,454.55 + $82,644.63 = $128,099.18 Year 3: $128,099.18 + $112,233.45 = $240,332.63 Year 4: $240,332.63 + $28,925.62 = $269,258.25 Year 5: $269,258.25 + $15,248.42 = $284,506.67 The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment of $200,000. In this case, it takes approximately 2.6380 years for the cumulative discounted cash flows to equal or exceed $200,000. Therefore, the correct answer is e. 2.6380 years.

Explanation
The correct answer is b. P21,937.26. To determine the present value of the investment, we need to discount each cash flow back to its present value using the required rate of return of 14 percent. The present value of the cash flows in Years 1-5 is calculated using the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the rate of return, and n is the number of years. The present value of the cash flows in Years 6-8 and Years 9-10 are calculated in the same way. Summing up all the present values gives us the total present value of the investment, which is P21,937.26.