Question

Benjamin and Stéphanie's mother/mother-in-law, Suzy, issued a $1 000 000 twenty-five year interest-only loan to the couple. Under the terms of the loan, they make annual payments of interest every year (at 3% p.a.); the final payment will consist of the regular interest amount together with the return of principal. Unbeknownst to the couple, Suzy has invested each interest payment at 3.5% p.a. Her intention is to give the accumulated amount to the couple when the loan matures. Allowing for this gift, what is Benjamin and Stéphanie's net payment to Suzy when the loan matures? Include in your answer • a fully labelled cash flow diagram (drawn from the perspective of Suzy's investment fund), • your chosen valuation date and • an equation of value.

Answer 1

Since under the loan they will pay interest on loan every year for 25 year and then pay the principal at the end of 25 years So the cash flow would be the annual interest payment plus principal at the end Year Now she invest each of the interest payment so first payment would be received at the end of year 1 and will be invested for 24 years 0 Year 3 4 5 12 Cash flow (1,000,000.00) 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 1,030,000.00 13 Interest 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 30,000.00 Total value of interest Interest*(1+ Interest) Time period 68,499.85 66,183.43 63,945.35 61,782.94 59,693.67 57,675.04 55,724.68 53,840.27 52,019.58 50,260.46 48,560.84 46,918.68 45,332.06 43,799.09 42,317.96 40,886.92 39,504.27 38,168.38 36,877.66 35,630.59 34,425.69 33,261.54 32,136.75 31,050.00 30,000.00 1,168,495.70 23 24 25 Now after 25 years Suzy will give them back 1,168,495, So the net payment on the day loan matures is (1168495.7-1030000) 138,495.70 They will receive this net amount, the time of the valuation would be year 25