Concept explainers
Pensacola Cablevision Company provides television cable service to two counties in the Florida panhandle. The firm’s management is considering the construction of a new satellite dish in December of 20x0. The new antenna would improve reception and the service provided to customers. The dish antenna and associated equipment will cost $200,000 to purchase and install. The company’s old equipment, which is fully
The new satellite dish will be depreciated under the MACRS depreciation schedule for the 5-year property class. The company’s tax rate is 40 percent.
Pensacola Cablevision’s president expects the real rate of interest in the economy to remain stable at 10 percent. She expects the inflation rate, currently running at 20 percent, to remain unchanged.
Required:
- 1. Compute the price index for each year from 20x1 through 20x7, using 1.0000 as the index for 20x0.
- 2. Prepare a schedule of after-tax cash flows measured in real dollars.
- 3. Compute the
net present value of the proposed new satellite dish using cash flows measured in real dollars. Use a real discount rate equal to the real interest rate.
1.
Calculate the price index of new satellite dish for each year.
Explanation of Solution
Cash inflows: The amount of cash received by a company from the operating, investing, and financing activities of the business during a certain period is referred to as cash inflow.
Cash outflows: The amount of cash paid by a company for the operating, investing, and financing activities of the business during a certain period is referred to as cash outflow.
Calculate the price index of new satellite dish for each year as follows:
Year | Price factor | Price factor for each year | Price index |
20x1 | 1.20 | (1.20)1 | 1.2000 |
20x2 | 1.20 | (1.20)2 | 1.4400 |
20x3 | 1.20 | (1.20)3 | 1.7280 |
20x4 | 1.20 | (1.20)4 | 2.0736 |
20x5 | 1.20 | (1.20)5 | 2.4883 |
20x6 | 1.20 | (1.20)6 | 2.9860 |
20x7 | 1.20 | (1.20)7 | 3.5832 |
Table (1)
Note: Normal price rate of 100% is taken as 1 and the inflation rate of 20% is taken as 0.20. Hence, the price factor is 1.20
2.
Prepare a schedule of after tax cash flow measured in real dollars.
Explanation of Solution
Prepare a schedule of after tax cash flow measured in real dollars as follows:
Cash outflow:
Cash inflows:
Schedule for the cash inflows | |||
Year | After tax operating cost savings (2) (F) |
Depreciation expense (1) (G) | After tax cash flow in real dollars |
20x1 | $42,000 | $13,333 | $55,333 |
20x2 | $42,000 | $17,778 | $59,778 |
20x3 | $42,000 | $8,889 | $50,889 |
20x4 | $42,000 | $4,444 | $46,444 |
20x5 | $42,000 | $3,704 | $45,704 |
20x6 | $42,000 | $1,543 | $43,543 |
20x7 | $42,000 | - | $42,000 |
Table (2)
Working note (1):
Calculate the depreciation expense under MACRS.
Depreciation Schedule | ||||||
Year |
MACRS Percentage (A) |
Depreciation |
Tax Rate (C) |
Depreciation expense |
Price index (E) |
Depreciation tax shield in real dollars |
20x1 | 20.00% | $ 40,000 | 40% | $16,000 | 1.2000 | $13,333 |
20x2 | 32.00% | $64,000 | 40% | $25,600 | 1.4400 | $17,778 |
20x3 | 19.20% | $38,400 | 40% | $15,360 | 1.7280 | $8,889 |
20x4 | 11.52% | $23,040 | 40% | $9,216 | 2.0736 | $4,444 |
20x5 | 11.52% | $23,040 | 40% | $9,216 | 2.4883 | $3,704 |
20x6 | 5.67% | $11,520 | 40% | $4,608 | 2.9860 | $1,543 |
20x7 | - | - | - | 3.5832 | - |
Table (3)
Working note (2):
Calculate the after tax incremental cash inflow.
Working note (3):
Calculate the after tax gain on sale of old equipment.
3.
Calculate the net present value of new satellite dish.
Explanation of Solution
Year |
Cash inflow (H) | Present value factor @10% (I) |
Present value |
20x1 | $55,333 | 0.909 | $50,298 |
20x2 | $59,778 | 0.826 | $49,377 |
20x3 | $50,889 | 0.751 | $38,218 |
20x4 | $46,444 | 0.683 | $31,721 |
20x5 | $45,704 | 0.621 | $28,382 |
20x6 | $43,543 | 0.564 | $24,558 |
20x7 | $42,000 | 0.513 | $21,546 |
Total present value | $ 244,100 | ||
Less: Cash outflow for investment | $ 188,000 | ||
Net present value | $ 56,100 |
Table (4)
Note: Refer Appendix A (table III) for the present value factor.
Therefore, the net present value of new satellite dish is $56,100.
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