What is the Net Present Value of this series of annual cash flows at an interest rate of 20% per year: Year 0:<$15,000>, Year 1: $2,000, Year 2: $0, Year 3: $15,000, Year 4 $0, Year 5 $18,000? (Note that the <> are used to indicate a negative number).
Answer(s): B
On the BAII Plus, press CF 2nd CLRWork 15000 +/- ENTER DownArrow 2000 ENTER DownArrow DownArrow 0 ENTER DownArrow DownArrow 15000 ENTER DownArrow DownArrow 0 ENTER DownArrow DownArrow 18000 ENTER DownArrow DownArrow 2nd Quit. Then press NPV 20 ENTER DownArrow CPT. On the HP12C, press these keys: 15000 CHS BlueShift CFo 2000 BlueShift CFj 0 BlueShift CFj 15000 BlueShift CFj 0 BlueShift CFj 18000 BlueShift CFj. Then press 20 i, YellowShift NPV. The "DownArrow" represents the downward-pointing arrow on the top row of the BAII Plus keyboard. Make sure the BAII Plus has the P/Y value set to 1.
For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what percent of the observations?
Answer(s): D
95% of the are under the curve will lie within plus and minus 2 standard deviations of the mean.
Assume you buy a car for $18,000 today and agree to pay $250 a month, beginning next month, for 5 years with a final payment also due 5 years from today to pay off any remaining balance. How large will that final payment be, if interest accrues at 2.9% per year, compounded monthly?
There are 60 months in 5 years. This is a problem known as a balloon payment. On the BAII Plus, press 60 N, 2.9 divide 12 = I/Y, 18000 PV, 250 +/- PMT, CPT FV. On the HP12C, press 60 n, 2.9 ENTER 12 divide i, 18000 PV, 250 CHS PMT, FV. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
After a sterling year, your boss has decided to reward you. She has offered you three alternatives:Take $28,000 right now.Take $2,500 bonus per month for the next 12 months, starting next month. Take $16,000 at the end of six months and another $15,000 at the end of the year. If your discount rate is 6% per year on a monthly compounded basis, how much is the present value of your bonus?
Answer(s): A
The discount rate per period (1 month) = 6%/12 = 0.5%. The present value of alternative B is (using the annuity formula) 2,500/0.005*[1 - 1/1.005^12] = $29,047. The present value of alternative C is trickier, since the rate you have been given is compounded monthly. Therefore, the PV of C is 16,000/1.005^6 + 15,000/1.005^12 = $29,656. So you should take alternative C and your bonus is worth $29,656.
Excess kurtosis is a problem for investment researchers using normal distributions because:
Historical returns are better modeled with fat-tailed (or leptokurtic) distributions, not platykurtic ones. If a researcher uses a normal distribution to model a fat-tailed distribution, the estimated probability of an extreme outcome will be underestimated. Thus, the frequency of market crashes will be underestimated, an underestimation of the volatility risk.
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