Discounted Cash Flow Valuation
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION
Solutions to Questions and Problems 10. To find the future value with continuous compounding, we use the equation: FV = PVeRt a. b. c. d. FV = $1,000e.12(5) FV = $1,000e.10(3) FV = $1,000e.05(10) FV = $1,000e.07(8) = $1,822.12 = $1,349.86 = $1,648.72 = $1,750.67
23. We need to find the annuity payment in retirement. Our retirement savings ends at the same time the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs. (Monthly installment and so monthly compounding: 30 years time 12 months equal to 360months) Stock account: FVA = Rs.700[{[1 + (.11/12) ]360 – 1} / (.11/12)] = Rs.1,963,163.82 Bond account: FVA = Rs.300[{[1 + (.07/12) ]360 – 1} / (.07/12)] = Rs.365,991.30 So, the total amount saved at retirement is: Rs.1,963,163.82 + 365,991.30 = Rs.2,329,155.11 Solving for the withdrawal amount in retirement using the PVA equation gives us: PVA = Rs.2,329,155.11 = C[1 – {1 / [1 + (.09/12)]300} / (.09/12)] C = Rs.2,329,155.11 / 119.1616 = Rs.19,546.19 withdrawal per month 26. This is a growing perpetuity. The present value of a growing perpetuity is: PV = C / (r – g) PV = Rs.200,000 / (.10 – .05) PV = Rs.4,000,000 39. We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are:
PV of Year 1 CF: PHP1,000 / 1.10 PV of Year 3 CF: PHP2,000 / 1.103 PV of Year 4 CF: PHP2,000 / 1.104 So, the PV of the missing CF is:
= PHP909.09 = PHP1,502.63 = PHP1,366.03
PHP5,979 – 909.09 – 1,502.63 – 1,366.03 = PHP2,201.25 The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is: PHP2,201.25(1.10)2 = PHP2,663.52 Calculating the
Solutions to Questions and Problems 10. To find the future value with continuous compounding, we use the equation: FV = PVeRt a. b. c. d. FV = $1,000e.12(5) FV = $1,000e.10(3) FV = $1,000e.05(10) FV = $1,000e.07(8) = $1,822.12 = $1,349.86 = $1,648.72 = $1,750.67
23. We need to find the annuity payment in retirement. Our retirement savings ends at the same time the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs. (Monthly installment and so monthly compounding: 30 years time 12 months equal to 360months) Stock account: FVA = Rs.700[{[1 + (.11/12) ]360 – 1} / (.11/12)] = Rs.1,963,163.82 Bond account: FVA = Rs.300[{[1 + (.07/12) ]360 – 1} / (.07/12)] = Rs.365,991.30 So, the total amount saved at retirement is: Rs.1,963,163.82 + 365,991.30 = Rs.2,329,155.11 Solving for the withdrawal amount in retirement using the PVA equation gives us: PVA = Rs.2,329,155.11 = C[1 – {1 / [1 + (.09/12)]300} / (.09/12)] C = Rs.2,329,155.11 / 119.1616 = Rs.19,546.19 withdrawal per month 26. This is a growing perpetuity. The present value of a growing perpetuity is: PV = C / (r – g) PV = Rs.200,000 / (.10 – .05) PV = Rs.4,000,000 39. We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are:
PV of Year 1 CF: PHP1,000 / 1.10 PV of Year 3 CF: PHP2,000 / 1.103 PV of Year 4 CF: PHP2,000 / 1.104 So, the PV of the missing CF is:
= PHP909.09 = PHP1,502.63 = PHP1,366.03
PHP5,979 – 909.09 – 1,502.63 – 1,366.03 = PHP2,201.25 The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is: PHP2,201.25(1.10)2 = PHP2,663.52 Calculating the