Question

Cowboy Recording Studio is considering the investment of $138,600 in a new recording equipment. It is estimated that the new equipment will generate additional cash flow of $20,500 per year for each year of its 8-year life and will have a salvage value of $13,500 at the end of its life. Cowboys’s financial managers estimate that the firm’s cost of capital is 10%. Use Table 6-4 and Table 6-5.(Use appropriate factor(s) from the tables provided. Round the PV factors to 4 decimals.)

Required:

1. Calculate the net present value of the investment.
2. Calculate the present value ratio of the investment.
3. What is the internal rate of return of this investment, relative to the cost of capital?
4. Calculate the payback period of the investment.

Answer 1

Net Present Value:

• PV of initial investment = -$138,600 x 1 = -$138,600
• PV of cash inflows of $20,500 for 8 years = $20,500 x 5.3350 = $109,367.50 [Note: Rounded PV factor to 4 decimals]
• PV of salvage value at year 8 = $13,500 x 0.4666 = $6,299.10
  NPV = -$138,600 + $109,367.50 + $6,299.10 = - $22,933.40

Present Value Ratio:

• PV of inflows / PV of initial investment = ($109,367.50 +,$6,297.75) / $138,600 = 0.8345

Internal Rate of Return

• As NPV is negative at 10% discount rate, let's interpolate a lower rate.
• NPV at 5% = $3,035.80 [by using the PV tables; please use the exact table provided in the question if any].
• NPV at 6% = -$2,827.85 [by using the PV tables; please use the exact table provided in the question if any].
• So, IRR is between 5% and 6%.
• IRR = 5% + $3,035.80 / $3,035.80 + $2,827.85) = 5.51%
  We get the same result if we use excel function of IRR too.

Payback Period of the Investment:

• The undiscounted cash flows were negative till year 6, and become positive by the end of year 7.
• So the payback period is 6 years + $15,600 / ($15,600 + $4,900) = 6.76 years. (It can also be 6 years and 278 days (rounded up from 6 years and 277.76 days)) [Calculation is demonstrated below]

Year	CF	Cumulative CF
0	-1,38,600.00	-1,38,600.00
1	20,500.00	-1,18,100.00
2	20,500.00	-97,600.00
0	20,500.00	-77,100.00
4	20,500.00	-56,600.00
5	20,500.00	-36,100.00
6	20,500.00	-15,600.00
7	20,500.00	4,900.00
8	34,000.00	38,900.00

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