Question

Your company's regional offices are located in Vancouver in a building rented for $850,000 per year (payable at the end of each year). The building is for sale for $ Y. The local branch of the Royal Bank is willing to provide a mortgage of $2,800,000 toward the purchase of the building. The duration of the mortgage is 20 years, at a yearly interest rate of 4%. The mortgage will have to be repaid by 20 equal yearly (end of year) payments of $X each. (These payments would cover both interest and principal, so that after the last payment the mortgage is fully discharged).

Your company requires the building for ten years. The estimated value of the building at the end of 10 years is $3,400,000, and the mortgage principal outstanding at that time is $P. The* yearly cost of owning the building (municipal tax, maintenance, etc.) is $300,000. MARR (the minimum attractive rate of return) for your company is 12%.

Determine:

(a)        the mortgage payments, x        (3 mark)

(b)        the mortgage principal owing at the end of 10 years, P        (3 madß)

(c)        the total amount of mortgage interest in the first ten years (d) the internal rate of return of this purchase (for your company) if Y =3,550,000 (10 marls)

(e) the maximum value of Y which would be (economically) acceptable for your company

Answer 1

(a) The annual payment formula = Loan * [r * (1+r)^t]/[(1+r)^t - 1] ; where r is the annual rate (4%) and t is the term of loan (20 years)

Hence we have annual payment = 2800000 * [4% * (1+4%)²⁰] / [(1+4%)²⁰ - 1] = 206,028.90

(b) Residual Loan Balance after k years is given by formula = Loan * [(1+r)^t - (1+r)^k]/[(1+r)^t - 1] ; plugging the values or r, t and k (10 )

Residual Loan = 2800000 * [(1+4%)²⁰ - (1+4%)¹⁰] / [(1+4%)²⁰ - 1] = 1,671,078.94

(c) Total Mortgage Interest in first 10 years = Annual Payment * 10 - Principal Repaid in 10 years = 10 * 206028.90 - (2800000 - 1671078.94) = 931,367.95

(d) IRR worksheet is as below

Hence we see that the IRR is 47.18% which is significantly higher than 12% MARR.

(e) The company would find it profitable to purchase the property till such time the IRR is atleast 12% which is to say that the NPV at 12% discount rate should be zero for that value of Y. Since the sum of present value of positive CF from Year 1 to 10 (discounted at 12%) is 2500179.74, hence for the NPV to be zero, the difference between the loan amount and property value should maximum be 2500179.74. Hence the maximum acceptable value of Y = 2500179.74 + 2800000 = 5,300,179.74