Question

a new laptop has just come onto the market that you estimate will have an equivalent annual cost of $500. you could sell your current laptop right away for $1 000, or you could spend $500 on an upgrade. at the end of this year, after the upgrade, it will have a resale value of $800, going down by $200 a year. once its salvage value reaches zero, its physical life is over. if both laptops provide equivalent functionality, when should you replace your current laptop? your marr is 5%.

Answer 1

To determine when to replace your current laptop, compare the equivalent annual cost of the new laptop to the cost of keeping and upgrading your current laptop. Use present value calculations to make the decision based on a 5% minimum attractive rate of return.

Step-by-step explanation:

To determine when to replace your current laptop, we need to compare the equivalent annual cost of the new laptop to the cost of keeping and upgrading your current laptop. The equivalent annual cost of the new laptop is $500. If you sell your current laptop right away, you will receive $1,000. However, if you choose to upgrade your current laptop, you will spend $500 on the upgrade and the laptop will have a resale value of $800 at the end of the year, decreasing by $200 each year until its salvage value reaches zero.

Now let's calculate the present value of each option. We'll use a 5% minimum attractive rate of return (MARR) as the discount rate.

If you sell your current laptop right away, the present value of the $1,000 you receive is:

PV = $1,000 / (1+0.05) = $952.38

If you choose to upgrade your current laptop, the present value is:

PV = ($800 / (1+0.05)) + ($600 / (1+0.05)^2) + ($400 / (1+0.05)^3) + ($200 / (1+0.05)^4) + ($0 / (1+0.05)^5) = $1,415.61

Since the present value of upgrading the current laptop is higher than the present value of selling it right away, it is more cost-effective to upgrade the current laptop. Therefore, you should replace your current laptop with the new laptop.