Question

One of the analysis techniques we have learned is how to construct a choice table, showing which option would be selected across a range of borrowing interest rates. Why would the preferred option change due to changing borrowing interest rates?

Answer 1

In a choice table analysis, we are trying to find out which choice (cashflow) has a higher NPV at a given rate. We will pick whichever has higher NPV. But note that I wrote 'at a given interest rate'. This is where the question comes in. The question is asking, between different options of cashflows/choices, why would NPVs change based on interest rates (and as the NPV will change, so will our preferred choice).

The NPV changes because NPV is a factor of three things= initial investment, cashflows and interest rate. As we know, the foruma for NPV is

NPV=Initial investment+Cashflow1/(1+r)+cashflow2/(1+r)²+.....+cashflown/(1+r)ⁿ

where r is the interest rate, n is the number of years.

Now lets assume in some given choices, the number of years are same. So that leaves the NPV to vary with cashflows and interest rates.

Now its becoming easier to see. Every set of cashflows will become positive or negative NPV at a particular rate. As we change the interest rate, the cashflow will either give us higher or lower NPV. Every cashflow will have different NPV at a differet interest rate. Since interest rate will change the NPV, it stands to reason that our choices will change too because we are looking at highest NPV. Between 3 cashflows, it is possible that choice 1 had highest NPV at 10% interest rate, but choice 3 has higher NPV at 15%. So our choice changes according to interest rate.