Question

You (many years ago) are deciding whether to upgrade your company's equipment from typewriters to computer technology at a cost of $2,500 per machine, and machines will be replaced one-to-one. The typewriter technology was able to output $8,000 per unit per year, and you expect the computers to be able to output $9526 per unit per year (forever), but render the typewriters completely worthless. What would the NPV be of making this upgrade, per upgraded unit? Assume a 12.3% interest rate. __________________

You can produce 1,000 umbrellas at a production cost of $1.75 per unit. Alternatively, you may produce 3,000 umbrellas at a cost of $2.25 per unit. Umbrella sales this year are highly dependent on weather, and you believe there is a 0.27 chance of high demand due to bad weather, and a (1-0.27) chance of low demand. If there is high demand, you can sell the umbrellas for $4, and if there is low demand, you can only get $2 per widget. How many umbrellas should you choose to produce if you remain uncertain about the weather? _________________

Carry out calculations to at least 4 decimal places. Enter percentages as whole numbers. Example: 3.03% should be entered as 3.03. Do not include commas or dollar signs in numerical answers.

Answer 1

Answer:

Upgrade cost = $2,500

Annual increase in output (Incremental out) in perpetuity = $9,526 -$8,000 = $1,526

Interest rate = 12.3%

PV (of perpetual constant cash flow) = $1,526 / 12.3% = $12,406.50

NPV = PV (of perpetual constant cash flow) - Upgrade cost = $12,406.50 - $2,500 = $9,906.50

NPV = $9,906.50

NPV 9906.50


Answer:

Expected price = Probability of high demand * Price of Umbrella in case of high demand + Probability of low demand * Price of Umbrella in case of low demand

= 0.27 * $4 + (1 - 0.27) * $2

= $2.54

Expected Contribution in case 1000 umbrellas are produced = 1000 * ( sales price per unit - production cost per unit )

= 1000 * (2.54 - 1.75)

= $790

Expected Contribution in case 3000 umbrellas are produced = 3000 * ( sales price per unit - production cost per unit )

= 3000 * (2.54 - 2.25)

= $870

Since expected contribution is higher of 3,000 umbrellas are produced, you should choose to produce 3,000 umbrellas

Number of umbrellas you should produce = 3000