Beryl's Iced Tea currently rents a bottling machine for $55,000 per year, including all maintenance expenses. It is considering purchasing a machine instead and is comparing two options: a. Purchase the machine it is currently renting for $150,000. This machine will require $21,000 per year in ongoing maintenance expenses. b. Purchase a new, more advanced machine for $260,000. This machine will require $19,000 per year in ongoing maintenance expenses and will lower bottling costs by $14,000 per year. Also, $36,000 will be spent up front training the new operators of the machine. Suppose the appropriate discount rate is 8% per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each year, as is the rental of the machine. Assume also that the machines will be depreciated via the straight-line method over seven years and that they have a ten-year life with a negligible salvage value. The marginal corporate tax rate is 40%. The NPV of renting the current machine is
Question
Beryl's Iced Tea currently rents a bottling machine for 150,000. This machine will require 260,000. This machine will require 14,000 per year. Also, $36,000 will be spent up front training the new operators of the machine. Suppose the appropriate discount rate is 8% per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each year, as is the rental of the machine. Assume also that the machines will be depreciated via the straight-line method over seven years and that they have a ten-year life with a negligible salvage value. The marginal corporate tax rate is 40%. The NPV of renting the current machine is
Solution
To calculate the NPV (Net Present Value) of renting the current machine, we need to consider the rental cost of $55,000 per year for 10 years, discounted at the rate of 8% per year.
The formula for NPV is:
NPV = ∑ [Rt / (1+i)^t] - C0
where:
- Rt is the net cash inflow during the period t
- i is the discount rate or return that could be earned on capital over the same period
- t is the number of time periods
- C0 is the initial investment
In this case, the net cash inflow (Rt) is the rental cost of -$55,000 (it's an outflow so we consider it as negative), the discount rate (i) is 8% or 0.08, and the initial investment (C0) is 0 because the machine is rented, not purchased.
So, the NPV of renting the machine for 10 years is:
NPV = ∑ [-$55,000 / (1+0.08)^t] for t from 1 to 10
This is a geometric series that can be summed up using the formula for the sum of a geometric series:
Sum = a * [1 - r^n] / [1 - r]
where:
- a is the first term of the series
- r is the common ratio
- n is the number of terms
In this case, a = -$55,000 / 1.08, r = 1/1.08, and n = 10.
So, the NPV of renting the machine for 10 years is:
NPV = -$55,000 / 1.08 * [1 - (1/1.08)^10] / [1 - 1/1.08]
This will give you the NPV of renting the machine.
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