Question

10) Barron has bequeathed a growing perpetuity to his grandson Arron through a Trust. The first payment will be S12,000 and will come at the end of the year. These payments will then grow at a rate of 5% each year forever thereafter. If the opportunity cost is 9.5%, what is the value of the bequest today? The Trustees have determined that the value of the bequest today is S280,000. discount rate did the Trustees use in figuring this value? a) b) What 11) Glenview Industries is considering building a new machine that will save them $1000 in costs at the end of the first year. Thereafter, the machine will begin to wear out, so the savings will decline at 2% per year forever. If the opportunity cost is 6% per year, what is value today of the cost savings generated by the new machine?

​​​​​​​

Answer 1

10)

The present value of perpetuity can be calculated using the following formula: PV = A/ (r-g).

The present value of cash flows and the discount rate used can be calculated as follows:

10 Timeline for the growing perpetuity will be as follows: $12,000 $12,000*1.05 10 2 3 Year 12 13 14 9.50% 15 16 17 Opportunity cost If A is the first payment amount, g is the growth rate of the perpetuity and discount rate is r, then Present value of perpetuity is given as follows: PV 19 21 Given the Following data: 23 24 $12,000 9.50% 5% 26 27 PV $266,666.67D22/(D23-D24) Hence the value of bequest today will be Ş266,666.67 31 32 Present value of perpetuity (PV) is given as follows: Given the following data: 35 36 37 38 39 $280,000 5% $12,000 using the above Equation -(A/PV)+g 41 42 43 9.29% -(D38/D36)+D37 Hence the discount rate used is 9.29%