Question

Find the present worth of $4000 the first year, increasing by $1000 per year. The interest rate is 8%, and n equals 5. Draw a cash flow diagram and show your work. A lottery pays the winner $1 million, in 20 equal payments of $50,000. The payments are received at the end of the year, and the winner's interest rate is 12%. What is the present worth of the winnings?

Answer 1

Solution 1: As the question does not states that whether Cashflows are inflows or outflows, it will be assumed as outflows Also it is assumed that cash flows are at the end of the year Statement showing Cash flows during the Year (end of the year) Year Particulars 1 1 2 3 4 5 a. Annual Outflow $ 4,000.00 $5,000.00 $ 6,000.00 $7,000.00 $8,000.00 b. PV factor @8% 0.9259 0.8573 0.7938 0.7350 0.6806 Present value (axb) $ 3,703.70 $4,286.69 $ 4,762.99 $5,145.21 $5,444.67 Total Present Value $ 23,343.27 Cash Flow Diagram Inflows Outflows $ 4,000 $ 5,000 $ 6,000 $ 7,000 $ 8,000 Also the solution if cashflows were at the beginning of the year: Statement showing Cash flows during the Year (begining of the year) Year Particulars 1 2 3 4 5 $ a. Annual Outflow $ 4,000.00 b. PV factor @8% 1.0000 Present value (axb) $ 4,000.00 Total Present Value $ 25,210.73 $5,000.00 0.9259 $4,629.63 6,000.00 $7,000.00 0.8573 0.7938 5,144.03 $5,556.83 $8,000.00 0.7350 $5,880.24 $

Solution 2. Year Amount (a) PV factor Product (axb) @ 12% (b) $ $ $ 50,000 50,000 50,000 50,000 $ 50,000 50,000 $ 50,000 50,000 $ 50,000 50,000 $ 50,000 50,000 $ 50,000 $ 50,000 50,000 50,000 50,000 $ 50,000 $ 50,000 $ 50,000 Present worth of winings 0.8929 $ 44,642.86 0.7972 $ 39,859.69 0.7118 $ 35,589.01 0.6355 $ 31,775.90 0.5674 $ 28,371.34 0.5066 $ 25,331.56 0.4523 $ 22,617.46 0.4039 $ 20,194.16 0.3606 $ 18,030.50 0.3220 $ 16,098.66 0.2875 $ 14,373.81 0.2567 $ 12,833.75 0.2292 $ 11,458.71 0.2046 $ 10,230.99 0.1827 $ 9,134.81 0.1631 $ 8,156.08 0.1456 $ 7,282.22 0.1300 $ 6,501.98 0.1161 $ 5,805.34 0.1037 $ 5,183.34 $3,73,472.18 $ $ :

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