How do you value a freehold property with a current rent of ₦500,000 p.a., an ERV of ₦750,000 p.a., a rent review every 4 years, a term yield of 7%, and a reversionary yield of 9%?

This is the present value of an annuity of ₦500,000 for 4 years at a 7% yield. The formula for Years' Purchase (YP) for a term certain is $\frac{1 - (1+i)^{-n}}{i}$.

\text{YP for 4 years at 7%} = \frac{1 - (1+0.07)^{-4}}{0.07} \text{YP for 4 years at 7%} = \frac{1 - (1.07)^{-4}}{0.07} \text{YP for 4 years at 7%} = \frac{1 - 0.762895166}{0.07} \text{YP for 4 years at 7%} = \frac{0.237104834}{0.07} \approx 3.3872119 $$\text{Value of Term} = \text{₦}500,000 \times 3.3872119 = \text{₦}1,693,605.95$$

This is the value of the ERV in perpetuity, effective from year 4, using the reversionary yield.

$$\text{Capital Value at year 4} = \frac{\text{ERV}}{\text{Reversionary Yield}}$$ $$\text{Capital Value at year 4} = \frac{\text{₦}750,000}{0.09} = \text{₦}8,333,333.33$$

This involves discounting the capital value from Step 2 back to the present day using the reversionary yield. The present value factor for a single sum is $(1+i)^{-n}$.

\text{PV factor for 4 years at 9%} = (1+0.09)^{-4} \text{PV factor for 4 years at 9%} = (1.09)^{-4} \approx 0.7084252 $$\text{Value of Reversion} = \text{₦}8,333,333.33 \times 0.7084252$$ $$\text{Value of Reversion} = \text{₦}5,903,543.33$$

The total value is the sum of the Value of the Term and the Value of the Reversion.

$$\text{Total Property Value} = \text{Value of Term} + \text{Value of Reversion}$$ $$\text{Total Property Value} = \text{₦}1,693,605.95 + \text{₦}5,903,543.33$$ $$\text{Total Property Value} = \text{₦}7,597,149.28$$

The total value of the freehold property is approximately:

$$\text{₦}7,597,149.28$$