Question

please show all work

Answer 1

Part (a)

Sale Price, P = 37 / unit

Variable cost, VC = 23 / unit

Fixed Cost, FC = 875,000

Book Depreciation per year, D = (capital cost - Salvage value) / Life of the asset = (780,000 - 0) / 8 = 97,500

Let's say accounting break even quantity is Q. Hence at this quantity Q,

Sales = Variable cost + Fixed cost + Depreciation

SP x Q = VC x Q + FC + D

Hence, 37Q = 23Q + 875,000 + 97,500

Hence, Q = (875,000 + 97,500) / (37 - 23) =  69,464

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Part (b)

C₀ = 780,000

Production quantity, Q = 92,000

Tax rate, T = 35%

Base case cash flow = Annual post tax cash flow, C = (Sales - VC - FC - D) x (1 - Tax rate) + D = (SP x Q - VC x Q - FC - D) x (1 - T) = (37 x 92,000 - 23 x 92,000 - 875,000 - 97,500) x (1 - 35%) + 97,500 = 302,575

This cash flow occurs as annuity. Time period, N = 8 year; discount rate, R = 15%

PV of C as annuity = C x [1 - (1+R)^(-N)] / R = 302,575 x [1 - (1+15%)^-8] / 15% = 1,357,751

Hence, Base Case NPV = -C₀ + PV of annual post tax cash flow as annuity = -C₀ + PV of C as annuity = - 780,000 + 1,357,751 = $  607,751

NPV is proportional to Sales figure though not directly. Higher sales figure will result into higher NPV. A decline in sales figure will lead a decline in NPV.

When Q goes down by 500 units, i.e.Q = 92,000 - 500 = 91,500

Annual post tax cash flow, C = (Sales - VC - FC - D) x (1 - Tax rate) + D = (SP x Q - VC x Q - FC - D) x (1 - T) = (37 x 91,500 - 23 x 91,500 - 875,000 - 97,500) x (1 - 35%) + 97,500 =  298,025

Decline in NPV = Base Case NPV - NPV calculated above = $ 607,751 - 298,025 = $ 309,726
So, the NPV has reduced by $ 309,726 when sales quantity reduces by 500 units

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Part (c)

OCF increase when variable cost decreases. Another way of saying the same is, when variable cost decreases, the Operative cash flows increase.

Let's say VC decrease by $ 1. Hence, VC = 23 - 1 = 22

Hence, operating cash flow, OCF = Annual post tax cash flow, C = (Sales - VC - FC - D) x (1 - Tax rate) + D = (SP x Q - VC x Q - FC - D) x (1 - T) = (37 x 92,000 - 22 x 92,000 - 875,000 - 97,500) x (1 - 35%) + 97,500 =  362,375
Hence, increase is OCF = 362,375 - 302,575 =  $ 59,800