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Q: Finance - Payback Period, NVP, IRR bonds ( Answered ,   0 Comments )
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 Subject: Finance - Payback Period, NVP, IRR bonds Category: Reference, Education and News Asked by: lostinpeoria-ga List Price: \$25.00 Posted: 27 Jun 2005 18:16 PDT Expires: 27 Jul 2005 18:16 PDT Question ID: 537622
 ```1. Using the information below, calculate the payback period and the NPV. Cost of Capital = 13% Initial Investment 100,000 Cash inflow 1 15,000 Cash inflow 2 20,000 Cash inflow 3 30,000 Cash inflow 4 35,000 Cash inflow 5 40,000 2. Using the information in question #7, the IRR is closest to: a. 3.5% b. 5.5% c. 10.5% d. 20.5% 3. How much should a \$1,000-face-value bonds sell for, assuming the following conditions: The bond pays a coupon of 7% The coupon payments are paid semi-annually. The required rate of return on similar-risk investments is 7%. The bond matures in 10 years```
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 Subject: Re: Finance - Payback Period, NVP, IRR bonds Answered By: livioflores-ga on 27 Jun 2005 19:55 PDT Rated:
 ```Hi lostinpeoria!! 1. Using the information below, calculate the payback period and the NPV. Cost of Capital = 13% Initial Investment 100,000 Cash inflow 1 15,000 Cash inflow 2 20,000 Cash inflow 3 30,000 Cash inflow 4 35,000 Cash inflow 5 40,000 Payback Period (PB) calculation give us an idea on how long it will take for a project to recover the initial investment. If Y is the year before the full recovery of the investment I, U is the unrecovered cost at the start of last year and CFi is the CF of the year Y+1 then: PB = Y + U/CFi The initial investment is \$100,000 and you will recover it during the fourth year, then: Y = 3 and U = \$100,000 - (\$15,000 + \$20,000 + \$30,000) = \$35,000 PB = 3 + \$35,000/\$35,000 = 4 years The payback period is 4 complete years. - NPV: Present Value (PV): CF1 CF2 CF5 PV = --------- + ---------- + ... + ---------- (1 + r)^1 (1 + r)^2 (1 + r)^5 Where r is the required return (13% or 0.13 in this case) Net Present Value (NPV): NPV = PV - I where I = Total Initial Investment First calculate the PV of the cash flows: PV = \$15,000/1.13 + \$20,000/(1.13)^2 + \$30,000/(1.13)^3 + \$35,000/(1.13)^4 + + \$40,000/(1.13)^5 = = \$13,274.34 + \$15,662.93 + \$20,791.50 + \$21,466.16 + \$21,710.40 = = \$92,905.33 NPV = PV - I = \$92,905.33 - \$100,000 = -\$7,094.67 (NEGATIVE!!) The net present value of this project is -\$7,094.67 . Since it is negative, you will lose money with this project. ------------------------ 2. Using the information in question #7, the IRR is closest to: a. 3.5% b. 5.5% c. 10.5% d. 20.5% NOTE: I am assuming that the "information in question #7" is the information in previous question. Whatever be the info the resolution method is the same. If you want you can post the correct info and I will show you the answer as a clarification. IRR is the discount rate r at which the NPV equals zero: NPV = PV - I = 0 Then IRR is the discount rate r at which: PV = I So you must find the r that solves the following equation: CF1 CF2 CF5 I = --------- + ---------- + ... + ---------- (1 + r)^1 (1 + r)^2 (1 + r)^5 You can use different ways to calculate the IRR, for example: -Trial & Error -Calculator -Computer (Excel spreadsheet) Here is a brief guide to do this using an MS Excel spreadsheet for this problem: 1) Select a column for the project's Cash flows (for example column "A"). 2) Input the project's Cash Flows starting from the initial investment (this is a negative input) and followed by the CF1 to CF4 cash flows, each one in one cell of the column. 3) Click on the cell where you want your IRR calculated (say B1). 4) Enter "=IRR(" (without the quotes) and then highlight the column A then close the parenthesis and hit enter. For the project A the column A will have: A1: -100,000 A2: 15,000 A3: 20,000 A4: 30,000 A5: 35,000 A6: 40,000 B1: =IRR(A1:A6) You will find that IRR = 10.48% . The correct answer is: c. 10.5% Note that the IRR is lower than the cost of capital (13%), this is why the NPV is negative and also indicates that this project is a bad idea. ----------------------- 3. How much should a \$1,000-face-value bonds sell for, assuming the following conditions: The bond pays a coupon of 7% The coupon payments are paid semi-annually. The required rate of return on similar-risk investments is 7%. The bond matures in 10 years Remember that the value of a bond is the Present Value of all the future payments (Coupons + Principal), the discount rate to calculate this PV is i = 7%: Coupon Payments = C = \$1,000 * 0.07 / 2 = \$35 (divided by 2 because the coupons are paid in a semiannually rate) The formula for the PV of the semiannually coupon payments is: PV coupons = Coupon/(i/2) * [(1 - (1 / (1+i/2)^(2*10)))] = = \$35/0.035 * [(1 - (1 / (1.035)^20))] = (use a calculator here) = \$497.43 Now we must calculate the PV of the principal payment, for this semiannual bond is: PV of principal = Face Value / (1+(i/2))^(2*10) = = \$1,000 / (1.035)^20 = (use a calculator here) = \$502.57 Bond value = PV coupons + PV of principal = = \$497.43 + \$502.57 = = \$1,000 You can get from selling the bond \$1,000 .As you have noted,the bond price is the same that the face value, this is because the coupon rate is similar to the required rate of return. For reference on this topic see: "4.2.2 - Basic bond valuation - Semiannual Interest": http://www.wfu.edu/users/palmitar/Law&Valuation/chapter%204/4-2-2.htm#semiannualinterest ------------------------------------------------------ I hope that this helps you. feel free to request for a clarification if you need it before rate this answer. Best regards, livioflores-ga```
 lostinpeoria-ga rated this answer: and gave an additional tip of: \$5.00 `Timely - very happy.`

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