A firm is considering spending $$29,000$ at Time $0$ to test a new product. Depending on the test results, the firm may decide to spend $$64,000$ at Time $1$ to start production. If the product is introduced and it is successful, it will produce aftertax cash flows of $$48,000$ per year for Years $2$ through $4.$ If it is unsuccessful, there will be no cash flow in Year $1,$ after which the project will be terminated. There are no recovery costs at the end of Year $4.$ The probability of a successful test and investment is $58$ percent. What is the net present value at Time $0$ given a discount rate of $16$ percent?

Multiple Choice

$$$$7,098\mathrm{.}65$

$$$$3,594\mathrm{.}43$

$$5,881\mathrm{.}15$

$$8,407\mathrm{.}70$

$$1,133\mathrm{.}15$