Question
In: Finance
Consider the following cash flows of two mutually exclusive projects for Tokyo Rubber Company. Assume the...
|
Consider the following cash flows of two mutually exclusive projects for Tokyo Rubber Company. Assume the discount rate for both projects is 10 percent. |
| Year | Dry Prepreg | Solvent Prepreg | ||||
| 0 | –$ | 1,830,000 | –$ | 815,000 | ||
| 1 | 1,113,000 | 440,000 | ||||
| 2 | 926,000 | 730,000 | ||||
| 3 | 763,000 | 416,000 | ||||
| a. |
What is the payback period for both projects? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) |
| b. |
What is the NPV for both projects? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) |
| c. |
What is the IRR for both projects? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
| d. |
Calculate the incremental IRR for the cash flows. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) |
Solutions
Expert Solution
a.
Calculation of Payback Period of both Projects:
Payback period helps to determine the time required to recover initial investment.
It is calculated as:
Payback Period: Total Initial Investment/ Annual Net Cash Inflow.
In case annual cash inflow is not uniform, we have to first calculate cummulative cash flow as given in solution:
| Project Dry | ||
| Year | Annual Cash Flow | Cummulative Cash Flow |
| 1 | 1113000 | 1113000 |
| 2 | 926000 | 2039000 |
| 3 | 763000 | 2802000 |
In the given project, you can see that initial investment is $ 1830000, which can be recovered in cash flow of second year:
Now Payback period will be calculated as:
=Year 1 + (1830000-1113000)/926000
= 1+ ( 717000/926000)
=1.774 years
(1830000-1113000) signifies additional cash flow required to recover initial investment and it is divided by $ 926000 i.e. cash flow earned in year 2 assuming it is earned uniformly over period
| Project Solvent | ||
| Year | Annual Cash Flow | Cummulative Cash Flow |
| 1 | 440000 | 440000 |
| 2 | 730000 | 1170000 |
| 3 | 416000 | 1586000 |
In the given project, you can see that initial investment is $ 815000, which can be recovered in cash flow of second year:
Now Payback period will be calculated as:
=Year 1 + (815000-440000)/730000
= 1+ ( 375000/730000)
=1.514 years
(b) Calculation of NPV of both projects
Net Present Value technique is a discounted cash flow technique that calculates the present value of cash flow earned from investment and compare it with Present Value of Cash outflow and If NPV is 0 or greater than 0 than it is accepted as required rate of return is achieved.
Calculation of NPV of both projects are as follow:
| Project Dry | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 10% (b) | Present Value (a*b) |
| 0 | -1830000 | 1 | -1830000 |
| 1 | 1113000 | 0.909 | 1011717 |
| 2 | 926000 | 0.826 | 764876 |
| 3 | 763000 | 0.751 | 573013 |
| Total | 519606 | ||
| Project Solvent | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 10% (b) | Present Value (a*b) |
| 0 | -815000 | 1 | -815000 |
| 1 | 440000 | 0.909 | 399960 |
| 2 | 730000 | 0.826 | 602980 |
| 3 | 416000 | 0.751 | 312416 |
| Total | 500356 |
NPV of Both Projects are positive in this case.
(c) Calculation of IRR of both Projects:
IRR technique determines the discount rate at which Present Value of Cash Inflow is equal to Present Value of Cash Outflow. Therefore it is not necessary that calculated discount rate is equal to desired discount rate. If our desired rate of return is achieved, then project is accepted.
Calculation is as follow:
Lower Rate + ((NPV at Lower Rate/ (NPV at Lower Rate- NPV at Higher Rate))*(HR-LR))
Project Dry
| Assume discount rate @ 25% | |||
| Project Dry | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 25% (b) | Present Value (a*b) |
| 0 | -1830000 | 1 | -1830000 |
| 1 | 1113000 | 0.800 | 890400 |
| 2 | 926000 | 0.640 | 592640.00 |
| 3 | 763000 | 0.512 | 390656.00 |
| Total | 43696.00 |
| Assume discount rate @ 30% | |||
| Project Dry | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 30% (b) | Present Value (a*b) |
| 0 | -1830000 | 1 | -1830000 |
| 1 | 1113000 | 0.769 | 855897.00 |
| 2 | 926000 | 0.592 | 548192.00 |
| 3 | 763000 | 0.455 | 347165.00 |
| Total | -78746.00 |
IRR = 25 +((43296/(43296-(-78746))*(30-25))
= 25+(43296/122042)*5
= 25+ 1.77
= 26.77 % approx
Project Solvent:
| Assume discount rate @ 40% | |||
| Project Solvent | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 40% (b) | Present Value (a*b) |
| 0 | -815000 | 1 | -815000 |
| 1 | 440000 | 0.714 | 314160 |
| 2 | 730000 | 0.510 | 372300.00 |
| 3 | 416000 | 0.364 | 151424.00 |
| Total | 22884.00 |
| Assume discount rate @ 45% | |||
| Project Solvent | |||
| Year | Annual Cash Flow (a) | Present Value Factor @ 45% (b) | Present Value (a*b) |
| 0 | -815000 | 1 | -815000 |
| 1 | 440000 | 0.690 | 303600 |
| 2 | 730000 | 0.476 | 347480.00 |
| 3 | 416000 | 0.328 | 136448.00 |
| Total | -27472.00 |
= 40 +((22884/(22884-(-27472))*(45-40))
= 40 +(22884/50356)*5
= 40 + 2.27
= 42.27 % approx
(d) Calculation of Incremental IRR
This technique is used, when there are two investment opportunties which are competitive in nature and further it involves different amount of investment.
Calculation is as follow:
| Year | Annual Cash Flow Project Dry | Annual Cash Flow Project Solvent | Difference in Cash Flow |
| 0 | -1830000 | -815000 | -1015000 |
| 1 | 1113000 | 440000 | 673000 |
| 2 | 926000 | 730000 | 196000 |
| 3 | 763000 | 416000 | 347000 |
| Assume Disc Rate 10% | |||
| Year | Differential Cash Flow (a) | Present Value Factor @ 10% (b) | Present Value (a*b) |
| 0 | -1015000 | 1 | -1015000 |
| 1 | 673000 | 0.909 | 611757.00 |
| 2 | 196000 | 0.826 | 161896.00 |
| 3 | 347000 | 0.751 | 260597.00 |
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