Question

Seong Hotels is interested in developing a new hotel is Seoul. The initial investment of the project is $20 million, but cashflows could differ if the government imposes a hotel tax. There is a 60% chance a hotel tax will be imposed and cash flows would be $2 million per year for 20 years. However, there is a 40% chance there will not be a tax imposed so cash flows would be $4 million per year for 20 years. They will not know if the tax will be imposed until next year. What is the project's expected NPV if they wait and implement the project one year from now? Cost of capital is 10%.

Answer 1

NPV if hotel tax is imposed

Present value of cash flows at the end of year 1(PV1) = 2 million * PVIFA

cost or capital , r = 10% = 0.10

PVIFA( 10% , 20 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.10)²⁰ - 1)/((1.10)²⁰*0.10)] = 8.5135637

PV1 = 2 million* PVIFA = 2*8.5135637 = 17.0271274

NPV1 = (PV1 - Initial investment)/(1.10) = (17.0271274-20)/(1.1) = -2.7026114 or -2.70 million

When tax is not imposed

Present value of cash flows at the end of year 1(PV1) = 4 million * PVIFA

cost or capital , r = 10% = 0.10

PVIFA( 10% , 20 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.10)²⁰ - 1)/((1.10)²⁰*0.10)] = 8.5135637

PV2 = 4 million* PVIFA = 4*8.5135637 = 34.0542549

NPV2 = (PV2 - Initial investment)/(1.10) = (34.0542549-20)/(1.1) = 12.776595 million or 12.78 million

Expected NPV = ( 0.60*NPV1) +(0.4*NPV2) = (0.6*-2.7026114 ) + (0.4*12.776595 ) =$ 3.489071287 million or $3.49 million