 # Time Value of Money | Nairametrics

Let us talk this week about the Time Value of Money (TVM). This is principle everyone one, not just finance or accounting folks should know about and apply. Yes, it involves math’s

TVM simply means cash in hand today is worth more than cash tomorrow, why? Because cash in the future will come under the influence of factors like inflation which will affect its purchasing power. TVM allows the investors to compare two separate cash streams, employing quantitative methods, and select the best option.

For instance, you live in a flat in Lagos, your rent is N1,000,000 per annum, paid two years in advance. your landlord, informs you he needs cash and is willing to accept rent payment in advance for N900,000 for two years per annum if you paid now. You have two choices, pay N2m in full next year, or Pay N1.8m now. Which option will you choose?

A good way to solve this question is to ask how much in interest would an investor earn if the N2m is invested in a bank, that rate becomes our discount rate. Then compare this to the cash offer made by the landlord. So, we have our tenor of 2 years, we assume an interest payment of 5% per annum if money is put in the bank, we know our Future Sum is N2m. we want to determine how must that N2m paid in the future will be worth today.

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This we determine with a Present Value calculation. Present Value (PV) is simply the current value of a future sum of money, at a predetermined rate of return. PV in our example is calculated as

Present Value =FV (1+R) ^n

FV is Future Value or N2m

R is the Discount rate or 5%

N is a period of 2

Thus, the PV of N2m invested for 2 years at 5% is N1,814,058.96. Now compare to N1,800,000 the landlord requested, we should not accept the landlords offer because the Present Value of N2m paid in two years is worth more than the value of N1.8m paid today.

Keep in mind we have no way of knowing what the interest rate in two years will be. Thus, it’s always a good idea to have a sensitivity analysis where we can project out scenarios on interest rates, thus we can project with 6% or 4%. The higher the discount value the lower the PV of the cash flow

PV can also be used for just planning when making any comparison of cashflows. For instance, if you had a daughter aged 5 who wished to go to Harvard when she is 18, and the cost of Harvard tuition is \$50,000. How much should you save as a one-time payment to a bank today, to have \$50k in your bank account in 13 years?

Present Value =FV (1+R) ^n

FV is Future Value or \$50

R is the Discount rate or 2%

N is the period of 13

You will have to save in bulk today \$38,651. What happens is the discount rate doubles to 4%, then your bulk payment today falls to \$30028.70.

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In our earlier example, we used a single lump sum and calculated the Present Value, what if the payments in future were not a lump sum but instead were spread out into the future, in a stream of equal payments called an Annuity. The principle will still be the same, but we change the formula and use the Present Value of an Annuity to calculate Present Value

You earn N500,000 a year, should you request a loan of N5,000,000 today at a 5% interest rate, or simply save N500,000 every year to get N5m and spend.

Again to answer this we have to compare 5m less 5%  in cash today to the present value of an N500,000 paid every month. Again, our equation

PV is Future Value or N500,000

PMT is each stream of payment of N500,000

R is the Discount rate or 5%

N is the period of 10

The PV is N386,000. This means you are better off borrowing N475,000 today (500K less 5% interest cost), as it has a higher value than N386,000.

Today, you can calculate PV on your phone, simply plug in the numbers. You don’t have to be a math’s guru, however, you must understand the working of TVM and its application in taking business decisions.

— to nairametrics.com