Question

Discounted Cash Flows

A. choose between a perpetuity of $45,000/year inflating at 2%/year and a lump sum payment of $1,255,000. Use a 5.5% discount rate. Use the box to explain your choice.

B. run NPVs and IRRs for three airplane fuel pumps. Use a 12% discount rate: Pump A costs $35,000 and saves the firm $5,000 each year for years 1-15 Pump B costs $35,000 and saves the firm $4,500 each year for ever Pump C costs $35,000 and saves $4,000 in year 1; this saving continues for ever, increasing 4% per year

C. provide a 25% guaranteed cash flow IRR to an airline flying to your airport. The airline's cash flows are minus $1 million at the start and positive $371,739 each year for years 1-4. Calculate the subsidy to be paid at the start. Explain your answer in the box provided.

D. calculate the implicit interest rate (IRR) of a computer lease. The computers cost $30,000 at the start and pay a yearly lease of $12,000 for years 1-3. The salvage value is $1,000 at the end of year 4. Explain your answer in the box provided. If the firm can borrow at 8.5% from the bank, should it borrow from the bank or lease?

Answer 1

A) Perpetuity pays for an infinite amount of time.

Here Given,

Discount Rate or cost of capital = 5.5%

Inflation Rate = 2%

Real Cost of Capital = 5.5% - 2% = 3.5%

So, Present Value of Perpetuity = 45,000 / 0.035 = 1,285,714.3 $

As, 1,285,714.3 > 1,255,000 ; then Perpetuity is better option than lump sum amount.

B) NPV for Pump A =

  

For Pump B,

The infinite cash flow of $4,500,

So, NPV for Pump B =

For Pump C,

NPV of C = (CF= Cash Flow, R = Discount Rate, G = Growth Rate )

  

From, All these 3 Airline Fuel Pumps, Pump C is a more profitable investment option.

C) If IRR is 25% guaranteed, then we have to find a cash inflow that has a zero NPV using a 25% discount rate. By using this rule and taking some try & error to get the exact amount where NPV will be 0.

You will find at X = 425,000 , NPV = 0

So, We have to provide subsidy at the start = 425000 - 371739 = $53,261

Hope it helps :)