The firm in the table below produces denim jeans and each unit of capital represents one sewing machine. The MRP for each of machines 10 through 14 is provided. Each sewing machine delivers a stream of MRPs beginning one year from now, for a total of 2 years. Suppose that after 2 years each sewing machine is worth nothing. $$\begin{array}{l}
\begin{array} { | l | l | }
\hline \text { Number of } & \text { Annual MRP } \
\text { Sew ing Machines } & \
\hline 10 & \$ 2000 \
\hline 11 & \$ 1800 \
\hline 12 & \$ 1600 \
\hline 13 & \$ 1400 \
\hline 14 & \$ 1200 \
\hline
\end{array}\
\text { TABLE 15- } 2
\end{array}$$
-Refer to Table 15- 2. If the interest rate is 4%, what is the present value of the 14th sewing machine (rounded to the nearest dollar)? Note that the stream of MRPs begins one year from now and lasts for 2 years.

Question

The firm in the table below produces denim jeans and each unit of capital represents one sewing machine. The MRP for each of machines 10 through 14 is provided. Each sewing machine delivers a stream of MRPs beginning one year from now, for a total of 2 years. Suppose that after 2 years each sewing machine is worth nothing. $$\begin{array}{l}
\begin{array} { | l | l | } 
\hline \text { Number of } & \text { Annual MRP } \
\text { Sew ing Machines } & \
\hline 10 & \$ 2000 \
\hline 11 & \$ 1800 \
\hline 12 & \$ 1600 \
\hline 13 & \$ 1400 \
\hline 14 & \$ 1200 \
\hline
\end{array}\
\text { TABLE 15- } 2
\end{array}$$
-Refer to Table 15- 2. If the interest rate is 4%, what is the present value of the 14th sewing machine (rounded to the nearest dollar)? Note that the stream of MRPs begins one year from now and lasts for 2 years.

Quizplus · Accepted Answer

The present value (PV) of the 14th sewing machine is calculated using the formula for the present value of an annuity: PV = MRP / (1 + r)^1 + MRP / (1 + r)^2, where MRP is $1200 and r is 0.04. Calculating gives: PV = 1200 / 1.04 + 1200 / (1.04)^2 = $2263 (rounded to the nearest dollar).

The Firm in the Table Below Produces Denim Jeans and Each