Deep South Sounds would like to spend $189,000 for new sound equipment. However, the company has a major loan maturing 3 years from today and needs this money at that time to avoid bankruptcy. The sound equipment is expected to increase the cash flows by $45,000 in the first year, $92,400 in the second year, and $40,000 a year for the following 3 years. Should Deep South buy the sound equipment at this time? Why or why not?
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To determine if Deep South Sounds should buy the new sound equipment, we need to consider the time value of money by calculating the net present value (NPV) of the cash flows from the equipment. This will help us establish if the future cash flows are worth the current investment of $189,000.
Net present value is calculated by discounting the future cash flows back to their present value and then summing those up. We need an appropriate discount rate to account for the time value of money and the risk of the investment. This is typically the company's cost of capital or a rate they deem acceptable as their return on investment. For this example, let's assume that the discount rate is 10%.
- Initial Investment at Time 0: -$189,000 - Cash flow at the end of Year 1: +$45,000 - Cash flow at the end of Year 2: +$92,400 - Cash flow at the end of Year 3: +$40,000 - Cash flow at the end of Year 4: +$40,000 - Cash flow at the end of Year 5: +$40,000
To get the present value of each cash flow, we use the formula:
PV = FV / (1+r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
Let's calculate the NPV:
PV (Year 1) = $45,000 / (1 + 0.10)^1 = $40,909.09 PV (Year 2) = $92,400 / (1 + 0.10)^2 = $76,198.35 PV (Year 3) = $40,000 / (1 + 0.10)^3 = $30,052.42 PV (Year 4) = $40,000 / (1 + 0.10)^4 = $27,320.38 PV (Year 5) = $40,000 / (1 + 0.10)^5 = $24,836.71