Question

do PW

Q5. [20 marks] For this question, X is the first two digits (from the right) of your student ID. Wolfpack Inc., a textile manufacturing company, is considering opening a production and shipping facility to keep up with demand for its pillows. The facility is expected to require an initial investment of $190,000 and will have a $36,000 salvage value after 5 years. Net annual revenue is estimated to be $100,000 while annual maintenance costs are estimated to be X% of the annual revenue. Determine how sensitive the decision to invest in the new facility is to the estimates of initial cost and annual revenues. Use a MARR of 4% per year and a 5 years study period (If your student ID number is even, use the PW method. Otherwise use the FW method)

Answer 1

Ans)- Since ‘X’ is not given,

Take X = 50 i.e. Annual maintenance costs is 50% of the annual revenue.

Given,

Initial investment (outflow) = $190,000

Salvage value (inflow)= $36,000

Annual revenue (Annual inflows) = $100,000

Annual maintenance costs (annual outflows) = 50% of 100,000 = 100,000*50/100 = $50,000

Net annual flows = annual inflows - annual outflows

                                = 100,000 – 50,000 = $50,000

Hence using Present worth (PW) method-

Present Worth (PW) = A, + A1 A2 + (1+r)1 (1+r)2 + An (1+r)"

Where,

A₀,A₁, A₃, … ,A_n are the cash flows at the end of year 0,1,2,…,n respectively.

r: interest rate

here,

n=5 , r=4% = 0.04

A₀ (initial investment) = 190,000, A₁ = A₂ = A₃ = A₄ = 50,000 (net annual inflows)

A₅ (inflow at the end of year 5) = last net annual inflow + salvage value

                                                        = 50,000 + 36,000 = 86,000

Now,

50,000 50,000 50,000 PW = -190,000 + + + (1 + 0.04)1 (1 + 0.04) . (1 + 0.04)3 50,000 86,000 + + (1 + 0.04)4 (1 + 0.04)5

PW = -190,000 + 48,077 +46, 227 + 44, 452 +42,735 + 70,688

Present worth (PW) = $62, 179

Since the present worth is significantly positive. Hence, we will invest in this project or the project is financially viable.