Question 26 of 27: After-Tax Cash Flows and NPV

Question 7.1: After-Tax Cash Flows and NPV (8 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Purchase (capital) cost = 0.7M at Year 0; salvage value = 0.1M realized at completion of mining (end of Year 4); cost of capital i = 10%.

Find. After-tax cash flow (ATCF) for each of Years 1–4, and the project NPV.

Approach. Compute ATCF = Revenue − Operating cost − Tax for each year (adding salvage in Year 4), then discount each year's ATCF at 10% and sum, netting off the Year-0 capital cost.

1. Year 1–3 ATCF. $$ATCF_1=1.000-0.400-0.159=0.441\text{M};\quad ATCF_2=1.000-0.400-0.1615=0.4385\text{M};\quad ATCF_3=1.000-0.400-0.1656=0.4344\text{M}$$
2. Year 4 ATCF (including salvage). $$ATCF_4=(1.000-0.400-0.1684)+0.100=0.4316+0.100=\boxed{0.5316\text{M}}$$
3. Discount each year's ATCF at i=10%. $$PV_1=\frac{0.441}{1.10}=0.4009\text{M};\ PV_2=\frac{0.4385}{1.10^2}=0.3624\text{M};\ PV_3=\frac{0.4344}{1.10^3}=0.3264\text{M};\ PV_4=\frac{0.5316}{1.10^4}=0.3631\text{M}$$
4. Net present value. Sum the discounted cash flows and subtract the Year-0 purchase cost: $$NPV=-0.700+(0.4009+0.3624+0.3264+0.3631)=-0.700+1.4528=\boxed{0.753\text{M CDN}}$$