$2\mathrm{.}2$ Net Present Value $($NPV$)$ of Both Projects

The Net Present Value $($NPV$)$ is calculated using the formula:

$$

$$

$$

$=$

$$

Cash$$inflow

$$

$($

$1$

$+$

$$

$)$

$$

$$

Initial$$investment

NPV$=$

$(1+$r$)$

t

Cash$$inflow

t

$$

$$

$$Initial$$investment

Where:

$$

$=$

$14$

$\%$

r$=14\%($desired rate of return$)$

$$

t is the year

Cash inflows for both projects $=$ R$3,100,000$ per year for $5$ years

Project A:

Initial cost $=$ R$4,800,000+$ R$300,000($installation$)=$ R$5,100,000$

Scrap value in Year $5=$ R$300,000$

Project B:

Initial cost $=$ R$5,100,000$

No scrap value

Step $1$: Use the Present Value $($PV$)$ factors from the $14\%$ table for each year

Year PV Factor $(14\%)$ Cash Inflows $($R$)$ PV of Cash Inflows $($Project A$)$ PV of Cash Inflows $($Project B$)$

$10\mathrm{.}87723,100,0002,719,3202,719,320$

$20\mathrm{.}76953,100,0002,385,4502,385,450$

$30\mathrm{.}67503,100,0002,092,5002,092,500$

$40\mathrm{.}59213,100,0001,835,5101,835,510$

$50\mathrm{.}51943,100,0001,610,1401,610,140$

Scrap value $300,0000$

PV factor $0\mathrm{.}51940\mathrm{.}5194\backslash$times $300,000=155,820$

Step $2$: Calculate the total PV of cash inflows

Project A:

Total$$PV$($cash$$inflows$+$scrap$)$

$=$

$2$

$,$

$719$

$,$

$320$

$+$

$2$

$,$

$385$

$,$

$450$

$+$

$2$

$,$

$092$

$,$

$500$

$+$

$1$

$,$

$835$

$,$

$510$

$+$

$1$

$,$

$610$

$,$

$140$

$+$

$155$

$,$

$820$

$=$

$10$

$,$

$798$

$,$

$740$

Total$$PV$($cash$$inflows$+$scrap$)=2,719,320+2,385,450+2,092,500+1,835,510+1,610,140+155,820=10,798,740$

Project B:

Total$$PV$($cash$$inflows$)$

$=$

$2$

$,$

$719$

$,$

$320$

$+$

$2$

$,$

$385$

$,$

$450$

$+$

$2$

$,$

$092$

$,$

$500$

$+$

$1$

$,$

$835$

$,$

$510$

$+$

$1$

$,$

$610$

$,$

$140$

$=$

$10$

$,$

$642$

$,$

$920$

Total$$PV$($cash$$inflows$)=2,719,320+2,385,450+2,092,500+1,835,510+1,610,140=10,642,920$

Step $3$: Calculate the NPV

NPV of Project A:

$$

$$

$$

$=$

$10$

$,$

$798$

$,$

$740$

$$

$5$

$,$

$100$

$,$

$000$

$=$

$$

$5$

$,$

$698$

$,$

$740$

NPV$=10,798,7405,100,000=$R$5,698,740$

NPV of Project B:

$$

$$

$$

$=$

$10$

$,$

$642$

$,$

$920$

$$

$5$

$,$

$100$

$,$

$000$

$=$

$$

$5$

$,$

$542$

$,$

$920$

NPV$=10,642,9205,100,000=$R$5,542,920$

NPV of Project A $=$ R$5,698,740$

NPV of Project B $=$ R$5,542,920$