Question

Self-insurance is being considered by a company to protect against damage and loss of its fixed capital investment. The fixed capital investment is $50,000. If self-insurance is used, a reserve fund will be setup under an ordinary annuity plan, where $400 is invested at the end of each year. Neglecting any charges connected with administration of the fund, how much additional money must be deposited in the fund at the beginning of the program, i.e. at the end of Year 0, in order to have sufficient funds accumulated to replace a $50,000 loss after 10 years? Assume all money in the fund, (i.e. initial single-payment investment and annual annuity investments) can be assumed to earn interest compounded annually with a nominal interest rate of 6%.

Answer 1

PV of annual payments = 400 x P/A(6%, 10) = 400 x 7.3601 = 2,944.04

PV of capital fund discounted back to year 0 = 50,000 x P/F(6%, 10) = 50,000 x 0.5584 = 27,920

Additional amount ($) = 27,920 - 2,944.04 = 24,975.96