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Questioned Before Shortlisted: Investment A or B?

The company is presented with two investment opportunities:
Investment A) We invest $1,000,000 and we are guaranteed to receive back $2,000,000 one year from now.
Investment B) We invest $5,000,000 and we are guaranteed to receive back $6,050,000 one year from now.
The risk profile for both investments is exactly the same. There is no strategic interest in pursuing one of the other. Which option would you take and why?

I came across the above question in an electronic application form for a certain job vacancy. I am not a fan of this kind of forms. As Liz Ryan put it, they are “talent-repelling” but they appear often. (I read her “How To Outwit An Online Job Application” some time ago.) Nevertheless, this question got my attention instantly and you can read my answer below. It gets more interesting as it has eventually disappeared in the form.

From the start, in money terms, A pays 2000000 – 1000000 = $1000000
B pays 6050000 – 5000000 = $1050000
Therefore, the return (in figure) of B is bigger than (that of) A.

However, in terms of the rate of return, A = 1000000 / 1000000 = 100%
B = 1050000 / 5000000 = 21%
The rate of return of A is much larger than (that of) B.

So it says that the risk profile is the same for both A and B. Are you forced to invest by some mysterious power? If not, the question that must be asked is: how high is the risk? If it is very high, then neither should be chosen!

If the risk is low, then a further question should be asked: does the company have the cash to invest? If it has $1m idle cash, only A can be chosen. If it has $5m, either A or B. If it has $6m or more, both should be chosen!

Note that I am talking about idle cash, which means that the cash is not needed for operation for 1 year. This means you need to make a cash budget (another name is cash flow forecast) to see if you have the surplus cash every month (or even every day) of the coming year. If at any time the projection turns negative, for example at the end of the 5th month, and the company is not aware of the problem beforehand, it may have to rush some cash at an undesirably high interest rate, or sell goods/services at a discount, or even a favour from another company/person. A cash favour can be more expensive than interest cost. The ultimate risk is that, while many companies closed because of not making enough profit to survive, still many others died from cash shortage at a certain time. Survival interest should kick in before strategic interest.

In order to answer this question, it is better narrowed down to:
If you have $5m idle cash, and “guaranteed” means no risk, which would you choose?
The obvious answer is B, because you get $50000 more, as you know the cash is idle anyway.
The “ratio” answer is A, because the rate of return is much higher (100% vs 21%).
I choose A for one more reason: no one knows for sure how the future is going to be. I wouldn’t lock up $4m cash flow just to get $50000 more, if I am already getting $1m return by investing $1m for a year.

As you can see, the question makes the answer complex. If this was the original intention to differentiate the candidates, probably it is ok. If not, the answer is quite simple as shown in the last part, and is fundamental to all financiers.

(post from my earlier blog in 2017)

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