Calculate the payback period accounting for inflation

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

25 July 2021

After last week’s explanation of the meaning of the time value of money, we are now ready to tackle the question that was sent in by Leonard Mwangi, which was: “What would be the right way to calculate the payback period of an investment while accounting for the time value of money? If I purchase a property at Sh5 million and the monthly rent is Sh35,000, what will be the payback period if the average inflation rate is 5 per cent over the years?”

If we ignore inflation, the problem is really easy: we divide the purchase price by the monthly rent to get the number of months required to recover the investment. This comes to about 143 months which is 11 years and 11 months. We can round this off to about 12 years.

From last week’s discussion, it is clear that the Sh35,000 of today will be worth less after such a long period of time. Using Leonard’s 5 per cent inflation rate and the illustration of pencils, we find that the price of one pencil will have risen from Sh10 to Sh17.96 in 12 years time.

Thus, after 12 years, Sh35,000 will only be enough to buy 1,949 pencils down from today’s 3,500. For this reason, we must knock down the purchasing power of the rent year-by-year. The total rent in the first year is Sh420,000 and this can buy 42,000 pencils.

In the second year, the Sh420,000 will buy fewer pencils: 40,000. Thus, at the end of two years, the cumulative rent will be equivalent to 82,000 pencils. Then in the third year, the Sh420,000 will buy 38,095 pencils and now the total is 120,095.

The number of pencils purchased every year is always fewer than those of the previous year. So now the question is: how many years will it take to accumulate the same number of pencils as would been bought by Sh5 million today? With Sh5 million, we can buy 500,000 pencils at Sh10 each. If we continue with the progression of the previous chapter, we find that it takes almost 18 years (17 years and 8 months) to get 500,000 pieces.

This is the inflation adjusted payback period. One assumption that we have made is that the rent remains constant throughout the 18-year period. This is grossly unrealistic. If we adjust the rent to keep up with inflation, then the payback period goes back to 11 years and 11 months.