NPV calculation

Question

This is from a casebook on whether a zoo should buy a zebra. below is info on revenue and cost.

Revenue:

•300K people visit the zoo annually; admission is $15 per person

•Benefits from zebra acquisition could lead to increased attendance. Another zoo that acquired a similar zebra had an 8% increase.

Costs from zebra acquisition:

•Immediate costs: Acquisition cost ($235K), new facilities ($850K), transportation ($110K)

•Annual maintenances: Food, health costs, and additional trainers ($90K)

•Discount rate = 20%, Assume that the immediate costs are paid today, and annual costs and benefits are realized beginning next year and sustained into perpetuity, even though the Zebra will not live on to perpetuity.

The answer is this:

Annual benefits = (300K)*($15)*(0.08) = $360K

•Upfront costs = $235K + $850K + $110K = $1.195M

•Annual costs = $90K

•NPV = -$1,195K + (($360K -$90K)/0.20) = $155K

My question: shouldn't the NPV = -$1,195k + (($360k-$90k)/1.2)=-970k if the zebra will not live on to perpetuity?

Answer 1

Hi there,

Q: My question: shouldn't the NPV = -$1,195k + (($360k-$90k)/1.2)=-970k if the zebra will not live on to perpetuity?

Your formula would be correct if the costs and benefits would just be realized the year after the immediate costs. However, the prompt says that the costs and benefits are realized in perpetuity.

When that’s the case, the value generated by an asset in perpetuity can be calculated with the perpetuity formula as follows:

V=FCF/(r-g)

Where

V = Value of the asset
FCF = Free cash flow
r= Discount rate
g= Growth rate of FCF

So the denominator in this case is r (discount rate) given g=0, and not (1+r).

The previous formula for the value of an asset in perpetuity is equivalent to the following:

You can check that using n=1 (that is the value for 1 year only after the immediate cost) you would get your formula. In this particular case, you would then have to add the immediate cost that would happen in n=0.

You can find a more detailed analysis of the perpetuity formula at the link below:

▶ How to Find the Net Present Value of a Company

Hope this helps,

Francesco

Answer 2

What a fantastic answer by Francesco. Can't beat that one :)

HEre are a few key things to keep in mind with NPV…these trip up a lot of candidates:

Make sure you understand annuity (year by year) versus perpituity
Remember that g (growth) is the growth rate on the cash flows themselves (the denominator)
R = discount rate which can be multiple things (hurdle rate, interest rate, etc.)
NPV already inherently accounts for alternative investment options

Answer 3

Hi there,

Just wanted to highlight that while you should know NPV, this type of cases is a deviation from what is expected in strategy case interviews.