# McKinsey PST Problem:

McKinsey McKinsey PST PST
Recent activity on Jan 14, 2018
5.6 k Views

Hi all,

I have a question from the sample McK PST they have on their website. I don't quite understand their explanation, so I decided to ask it here.

If total Innovation Capital in Exhibit 1 (now at 13.8) were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in Human Capital (now at 3.3) that would see it represent more than half of total Innovation Capital in 10 years?

A: 10% B: 15% C: 20% D: 25%

NOTE: Innovation Captial is comprised of three different kinds of 'Capital' and the question is concerned with Human Capital.

How does one calculate this? Thanks

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Hey Paul,

first, you need to compute the value of innovation capital in 5 years: 13.8 * 1.05 ^ 5 = 17.6 (it's always about adding 5% each year 5 times)

then you need to try to check what are the potential values of human capital in 5 years time for the different options. Then lower percentage one that still allows you to reach a value which is higher than 8.8 (half of 17.6) is the right choice (you need to test the several options, as a tip i would start by trying out option b - in trial questions is better to start by middle options)

best

Bruno

A few questions actually. How do you do 13.8 * 1.05^5 ? Do you do this for each year? 13.8 * 1.05 = 14.49 * 1.05 = 15.21 * 1.05 = 15.97? And so on? This seems very time consuming, even for the PST. Doing this for 10 years would be even more time consuming. And I also don't really understand the second part of the explanation, can you please rephrase it?

(edited)

Paul, there are two shortcuts that might help you in some of these problems (but I don't believe any of them would be particular useful in this particular example). First, for small annual growth rate values and short period of times, you can get a ballpark estimate by linearly multiplying the growth rate by the number of years (in this case 5 * 5% = 25%, which will give 13.8 * 1.25 = 17.25; quite near the absolute value of 17.6). Second, you could use the rule of 72, which tells you that a number will take 72/growth rate to double up (at a 5% growth rate, the initial number will double in approximately 14.4 years).

(edited)

Regarding the second part of the explanation, you will need to do an iterative process of elimination. 3.3 * 1.15 ^5 = 6.63, so less than half of the other type of capital (17.6). Repeat the same for 20% and still less, so it will only work for 25% (3.3 * 1.25 ^5 = 10.08). In this case, using the proxy method I described before would give you a wrong answer, because the numbers are all very similar

I understand how to answer this question. Essentially you calculate the growth of Innovation Capital over 10 years at a 5% interest rate, and then see how much Human capital needs to grow to comprise 50% of that found figure. I guess my problem is that calculation 1.05*1.05*1.05.... ten times, seems so time consuming. And if shortcuts don't really work, how else to approach it?

How 1.05 came

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