Suppose you work for one of the big consulting firms (e.g., McKinsey or Boston C

ID: 2750548 • Letter: S

Question

Suppose you work for one of the big consulting firms (e.g., McKinsey or Boston Consulting) and Maytag has just hired your firm to tell them what to do in the case of the following: Maytag knows that they can produce a washing machine for $300, which covers all costs and profit. Sales are down, and they believe that adding a really attractive warranty might boost sales. They want you to tell them what they should add to the $300 to cover the risk resulting from adding the following warranty: if the machine fails within the first 6 years, the pro rata amount of the price is returned. For example, if it fails after 4.5 years, then (6- 4.5)/6=1.5/6 of the actual price P will be returned. (P equals 300 plus the present value of the warranty.) Based upon data that they provide, you decide that an exponential distribution with a mean lifetime of 10 years describes the lifetime of their washing machines quite well. You also decide to use a valuation rate r=.08. Based upon this information, derive a value of the warranty to be added to the $300, resulting in the actual price P

Explanation / Answer

In this question we will have to consider 2 factors while calculating price of warranty & thus price of washing machine.

1. Present value of amount to be paid to the customer if the machine fails in the warranty period i.e. 6 years this is calculated using Discounted Cash Flow method(DCF).

Present Value,PV=300

DCF=CF1/(1+r)^1 + CF2/(1+r)^2 + ............ CFt/(1+r)^t

As we know r= 0.8 and the warranty period extends till t=6 so we will get values mentioned in Row 3 of below table while calculating CF value excluding their probability. The value in Row 2 represents payout amount which is prorata basis for example payout in year 4 will be 300*(6-4)/6= 100 & so on.

2. Now this takes us to the second factor i.e. probability of machine failure happening thus leading to exponential Probability distribution with mean 10.

F(x, )= e^- x when x is positive which is in this case(x -> time)

Here = 1/mean & x will be 10-t.

So this distribution will come out to be as shown in Row 4

Years

Payout

250

200

150

100

CFt

231.4815

171.4678

119.0748

73.50299

34.02916

Probability

0.040657

0.044933

0.049659

0.054881

0.060653

0.067032

DCF

9.411335

7.704543

5.913081

4.033929

2.063973

Value of warranty(Sum of Row 5)

29.12686

So the value of Washing machine will be $ 329.12 (300 + warranty value)