$3\mathrm{.}1$ After$-$Tax Cash Flows and Net Present Value

Lease Option:

The after$-$tax cash flows for the lease option can be calculated as follows:

Calculate the after$-$tax lease payments: Annual lease payment $=$ R$255,000$ After$-$tax lease payment $=$ Annual lease payment $*(1-$ Tax rate$)$ After$-$tax lease payment $=$ R$255,000*(1-0\mathrm{.}30)$ After$-$tax lease payment $=$ R$178,500$

Calculate the after$-$tax salvage value: Salvage value $=$ R$84,000$ After$-$tax salvage value $=$ Salvage value $*(1-$ Tax rate$)$ After$-$tax salvage value $=$ R$84,000*(1-0\mathrm{.}30)$ After$-$tax salvage value $=$ R$58,800$

Calculate the after$-$tax maintenance and insurance costs: After$-$tax maintenance cost $=$ R$2,800*12*(1-$ Tax rate$)$ After$-$tax maintenance cost $=$ R$33,600*(1-0\mathrm{.}30)$ After$-$tax maintenance cost $=$ R$23,520$ After$-$tax insurance cost $=$ R$1,100*12*(1-$ Tax rate$)$ After$-$tax insurance cost $=$ R$13,200*(1-0\mathrm{.}30)$ After$-$tax insurance cost $=$ R$9,240$

Calculate the after$-$tax cash flows for each year: Year $1$: After$-$tax lease payment $+$ After$-$tax maintenance cost $+$ After$-$tax insurance cost Year $1$: R$178,500+$ R$23,520+$ R$9,240$ Year $1$: R$211,260$ Year $2$ and $3$: After$-$tax lease payment $+$ After$-$tax maintenance cost $+$ After$-$tax insurance cost Year $2$ and $3$: R$178,500+$ R$23,520+$ R$9,240$ Year $2$ and $3$: R$211,260$

Calculate the net present value $($NPV$)$ of the cash outflows for the lease option using the after$-$tax cash flows and the after$-$tax salvage value.

Buy Option:

The after$-$tax cash flows for the buy option can be calculated as follows:

Calculate the after$-$tax maintenance and insurance costs: After$-$tax total maintenance and insurance cost $=$ R$75,000*(1-$ Tax rate$)$ After$-$tax total maintenance and insurance cost $=$ R$75,000*(1-0\mathrm{.}30)$ After$-$tax total maintenance and insurance cost $=$ R$52,500$

Calculate the after$-$tax running costs for each year: Year $1$: After$-$tax running cost $=$ R$55,000*(1-$ Tax rate$)$ Year $1$: R$55,000*(1-0\mathrm{.}30)$ Year $1$: R$38,500$ Year $2$: R$38,500*(1-0\mathrm{.}05)$ Year $2$: R$36,575$ Year $3$: R$36,575*(1-0\mathrm{.}05)$ Year $3$: R$34,746\mathrm{.}25$

Calculate the after$-$tax salvage value: After$-$tax salvage value $=$ R$150,000*(1-$ Tax rate$)$ After$-$tax salvage value $=$ R$150,000*(1-0\mathrm{.}30)$ After$-$tax salvage value $=$ R$105,000$

Calculate the after$-$tax cash flows for each year: Year $1$: After$-$tax total maintenance and insurance cost $+$ After$-$tax running cost Year $1$: R$52,500+$ R$38,500$ Year $1$: R$91,000$ Year $2$: R$52,500+$ R$36,575$ Year $2$: R$89,075$ Year $3$: R$52,500+$ R$34,746\mathrm{.}25$ Year $3$: R$87,246\mathrm{.}25$

Calculate the net present value $($NPV$)$ of the cash outflows for the buy option using the after$-$tax cash flows and the after$-$tax salvage value.

$3\mathrm{.}2$ Recommendation

Based on the calculated net present values $($NPVs$)$ for both options, the option with the higher NPV would be the more favorable choice. The option with the higher NPV would indicate the alternative that provides the most value to the company. Therefore, the option with the higher NPV should be recommended for selection.