Question

1. Using the data provided, calculate the capitalization rate and the value using direct capitalization under each of the following methods: (10 points)

                        NOI:                                        $14,000

                        Typical Loan Terms               75% loan to value ratio

                                                                        8.5% interest

                                                                        20 year amortization monthly

                        Equity Dividend Rate:                        6%

                        Loan Amount:                         $90,000

                        Risk Free Rate                        2.5

                        Premium for Risk                   3%

                        Premium for Illiquidity           2%

                        Premium for Management      1%

Band of Investment Technique:

           

Summation Method:

Answer 1

Calculation of Capitalization Rate and the value using direct capitalization under following methods :

1. Band of Investment Technique:

In this method we need to calculate the the effect of cost of loan ( debt cost ) with cost of equity.

Step 1 : Calculation of monthly amortization rate

= 8.5% interest / 12 months

= 0.7083% monthly interest rate or monthly amortization rate

Step 2 : Calculation of Annual mortgage or amortization constant

Annual Amortization Constant = (12 months x monthly amortiztion rate) / ( 1 - 1/ ( 1+ monthly amortization rate )Period)

Here, period is 240 months ( 20 years x 12 months )

Annual Amortization Constant = ( 12 months x 0.7083 % ) / ( 1 - 1 / ( 1 + 0.7083% )240)

Annual Amortization Rate = 8.5% / ( 1- 0.183796 )

Annual Amortization Rate = 0.085 / 0.8162 = 0.1041 i.e 10.41%

Step 3 : Calculation of Capitalization Rate under Band of Investment Technique

It is given that 75% is loan to value ration therefore 25% is contributed from equity

Capitalization Rate under Band of Investment Technique = Cost of Debt x Portion of Debt + Cost of Equity x Portion of Equity

= 10.41% x 0.75 + 6% x 0.25 = 7.8075% + 1.5% = 9.3075%

Capitalization Value under Band of Investment Technique = Net operating Income ( NOI ) / Capitalization Rate

= $ 14,000/ 9.3075% = $ 150,416.33

2.Summation Method :

In this method we should consider all risks of the business with risk free return in the market. Investor should expect the return beyond the risk free return and the risks availling in the business therefore we added all risks factors for calculating capitalization rate.

Capitalization rate = Risk free return + Premium on risks in the business

In the given case

Capitalization Rate as per Summation Method = Risk free rate of return + premium for risk + premium for liquidity + Premium for Management

Capitalization Rate as per Summation Method = 2.5% + 3% + 2% + 1% = 8.5%

we consider factors as premium for risk as it is expected market return over risk free return for investment , premium for liquidity as to equalize the liquidity in the business, premium for management as management inputs will direct the organization to earn the desired return.

Capitalization Value as per Summation Method = Net Operating Income / Capitalization Rate as per Summation Method

Capitalization Value as per Summation Method = $ 14,000 / 8.5% = $ 164,705.88