Question

solve these question by financial concepts ?

3.     You think that you will be able to deposit SR4000 at the end of each of the next (3) years in a bank account paying 8% rate of return. Ypu currently have SR7000 in the account. How much will you have in (3) years? In (4) years?

4.     If a nurse deposits $1,000 today in a bank account and the rate of return is compounded annually at 12 percent, what will be the value of this investment five years from now

5.     The CFO of a home health agency needs to determine the present value of a $5,000 investment received at the end of year 10. What is the present value if the discount rate is 15%

6.     If a hospital were to receive $4,000 in payments per year at the end of each year for the next 12 years from an uninsured patient who underwent an expensive operation, what would be the current value of these collection payments given that he discount rate is 12%?

7.     Upon the untimely and tragic death of their wealthy aunt, the heirs wanted to memorialize her with a named donation to the local hospital. They offered the hospital a choice of $30,000 annual payments for 50 years or a lump sum payment of $400,000 today.

Ø What should be the decision if the hospital thinks it could earn an average of 4 percent annually on this donation?

Ø What should be the decision if the hospital thinks it could earn an average of 8 percent annually on this donation?

Ø What should be the decision if the hospital thinks it could earn an average of 12 percent annually on this donation?

8.     Williamsburg Nursing Home is investing in a restricted fund for a new assisted-living home. How much do they need to invest each year in order to earn $5,000,000 after 15 years if the expected rate of return on the investment is 10 percent?

Answer 1

Ans 3. Beginning Balance = SR7000

Deposit = SR3000 at the end of year 1, 2 & 3

Interest = 8%

Balance at the end of 3 years = 7000 * (1+8%)^3 + 3000 * ((1+8%)^2 – 1)/8%) * (1+8%) + 3000 = SR18557.18

Balance can also be calculated using the alternate value

= 7000 * (1+8%)^3 + 3000 * (1+8%)^2 + 3000 * (1+8%) + 3000 = SR18557.18

Balance at the end of 4 years = 7000 * (1+8%)^4 + 3000 * ((1+8%)^3 – 1)/8%) * (1+8%) = SR20041.76

Balance can also be calculated using the alternate value

= 7000 * (1+8%)^4 + 3000 * (1+8%)^3 + 3000 * (1+8%)^2 + 3000 * (1+8%) = SR20041.76

Ans 4.

Amount of deposit = $1000

Interest = 12% compounded annually

Time = 5 years

Value at the end of 5 years = $1000 * (1+12%)^5 = $1762.34

Ans 5. Value at the end of year 10 = $5000

Discount rate = 15%

Current Value = 5000/(1+15%)^10 = $1235.92

Ans 6. Amount of receipt = $4000 at the end of each year for 12 years

Discount rate = 12%

Present Value = 4000 * ((1-(1+12%)^-12)/12%) = $24777.50

Ans 7

Option 1: $30000 annual payment for 50 years

Option 2: $400000 today

We can compare the present values, by calculating the present value of option 1 by using rate of return of hospital as discount rate. Hence,

Since it is not clear that whether the payments of $30000 are made at the beginning of year or end of year, we are showing the calculation of both:

PV at 4% (end of year payments) = 30000 * ((1-(1+4%)^-50)/4%) = $644465.54

PV at 4% (beginning of year payments) = PV (end of year payments) * (1+4%) = $ 670244.16

Hospital would prefer annual payment of $30000

PV at 8% (end of year payments) = 30000 * ((1-(1+8%)^-50)/8%) = $367004.54

PV at 8% (beginning of year payments) = PV (end of year payments) * (1+8%) = $396364.90

Hospital would prefer annual payment of $30000

PV at 12% (end of year payments) = 30000 * ((1-(1+12%)^-50)/12%) = $249134.95

PV at 12% (beginning of year payments) = PV (end of year payments) * (1+12%) = $ 279031.15

Hospital would prefer one time payment of 400000

Ans 8

Amount to be invested each year = A

Time = 15 years

Rate of return = 10%

Future value of deposits = 5,000,000

Hence,

5,000,000 = A * ((1+10%)^15-1)10%) * (1+10%)

A = 5000000 / ((1+10%)^15-1)10%) * (1+10%)

A = $143062.6