Please show work and no excel, having trouble with figuring out which steps to c
ID: 2658258 • Letter: P
Question
Please show work and no excel, having trouble with figuring out which steps to complete first when solving the formula,
1.A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 4.5%, what is the present value of this prize?
2.An insurance policy offers you the option of being paid $750 per month for 20 years or a lump sum of $50,000. Which has the greater value if the current rate of return is 4.5% compounded monthly and you expect to live for 20 years?
3.Use the bond yield calculator to determine the yield of a bond that has 5 years to maturity (therefore ten semesters to go), has a coupon interest of 6% and a market price of $102.5.
Explanation / Answer
(1) Annual Payout = $ 50000, Tenure = 20 years and Rate of Return = 4.5 % per annum
PV of Annual Payouts = 50000 x (1/0.045) x [1-{1/(1.045)^(20)}] = $ 650396.823 approximately.
(2) Lumpsum Payment = $ 50000
Monthly Payments = $ 750, Rate of Return = 4.5 % per annum or 0.375 % per month
Tenure = 20 year or 240 months
PV of Monthly Payments = 750 x (1/0.00375) x [1-{1/(1.00375)^(240)}] = $ 118549.0776
Hence, the mothly payout value is greater,
(c) Tenure = 5 years or 10 half-years, Annual Coupon = 6 %, Market Price = $ 102.5 and Par Value = $ 100 (assumed)
Let the YTM be 2R
Semi-Annual Coupon = 0.06 x 100 x 0.5 = $ 3
Therefore, 102.5 = 3 x (1/R) x [1-{1/(1+R)^(10)}] + 100/(1+R)^(10)
Using trial and error/bond yield calculator/EXCEL's goal seek to solve the above equationwe get:
R = 0.0271 or 2.71 %
YTM = 2 x R = 2 x 2.71 = 5.42 %