Question

1) Bob is considering buying a home and selling it in one year. At t=0 he buys a house, the price is $100,000. At t=1 the house appreciates (i.e. the price goes up) by 20%, and Bob sells it.

Bob also pays transaction costs: buying costs are 5% of buying price, selling costs are 8% of selling price. Each time period is a year. Bob does not take any mortgages. Find the NPV of this project if the interest rate is 4%.

2)Find the IRR of Bob’s investment in the previous question.

Answer 1

Solution:

The values proived in the question are,

Initial Investment = $100,000

Future growth 20%, so selling price is $120,000

Buying cost = 5% of Buying price. That is $5000

Selling cost = 8% of Selling price. That is $9600

1) Calculating NPV, if the interest rate is 4%

The formula to calculate present value PV = FV/(1+r)^n

where, FV - Future Value

r - interest rate

n - time duration

and the formula to calculate NPV is sum of all present values of all cash flows (in & out).

Year	Cash Flow	Present Vale (PV = FV/(1+r)^n)
0	($100,000.00)	($100,000.00)
0	($5,000.00)	($5,000.00)
1	$120,000.00	$115,384.62
1	($9,600.00)	($9,230.77)
Net Present Value	$1,153.85

Hence, the NPV of this project is $1153.85

2) Calculating IRR,

The IRR is that rate which gives the project NPV of zero. (That is, it equates sum of cash flows to sum of present value of cash flows)

Year	Cash Flow	Present Vale, if IRR 5%	Present Vale, if IRR 6%
0	($100,000.00)	($100,000.00)	($100,000.00)
0	($5,000.00)	($5,000.00)	($5,000.00)
1	$120,000.00	$114,285.71	$113,207.55
1	($9,600.00)	($9,142.86)	($9,056.60)
Net Present Value	$142.86	($849.06)

if IRR is 5%, the NPV will be $142.86

If IRR is 6%, the NPV will be ($849.06)

The formula for calculating IRR = LR + [NPV@LR/NPV@LR - NPV@HR * (HR-LR)]

where, LR - Lower Rate

HR - Higher Rate

NPV@LR- NPV at Lower Rate

NPV@HR - NPV at Higher Rate

IRR for Project,

= 5 + [142.86 / (142.86 - (-849.06)) * (6-5)]

= 5 + [142.86 / 991.92]

= 5 + 0.1440

= 5.1440

Hence, IRR is 5.1440%